We report on the extraction of $R=\frac{\sigma_L}{\sigma _T}$ from
CCFR $\nu_\mu$-Fe and $\nub_\mu$-Fe differential cross sections.
The CCFR differential cross sections do not show the deviations
from the QCD expectations that are seen in the CDHSW data at
very low and very high $x$. $R^\nu$ as measured in $\nu_\mu$
scattering is in agreement with $R^{\mu/e}$ as measured in muon and
electron scattering. All data on $R$ for $Q^2 > 1$ GeV$^2$
are in agreement with a NNLO QCD calculation which includes
target mass effects. We report on the first measurements of $R^\nu$
in the low $x$ and $Q^2 < 1$ GeV region (where an anomalous large
rise in $R^{e}$ for nuclear targets has been observed by the
HERMES collaboration).

The results of the studies on bottom production in two-photon
events taken at LEP-2 are summarized.
Inclusive production has been studied at E_cms = 189-202GeV.
The measurements are compared to next-to-leading order calculations.
The theoretical predictions are significantly below the data.
The eta-b pseudoscalar meson has been search for via its exclusive
production. A limit on the production rate is given.

The potential to measure the structure of the photon at a high energy
e+e- linear collider (LC) will be presented. A LC will allow for a
special mode where the electron beams can be converted in high
energy photon beams, leading to a photon collider. With such a
collider the photon structure funtion can be measured down
to $x$ = a few times $10^{-5}$, and $Q^2$ up to $10^{5}$ GeV$^2$.
This give a large lever arm for QCD measurements, and charged current
events will allow to disentangle parton distributions of different
flavour. Also the nominal e+e- mod of an LC allows for photon structure
function measurements, beit in a somewhat reduced kinematical range
compared to a photon collider.

Inclusive e+/-p~single and double differential cross sections for
neutral current (NC) and charged current (CC) processes are measured
with the H1 detector at HERA, in the range of four-momentum transfer
squared, Q2, between 100 and 30000~GeV2 and Bjorken x between
0.0013 and 0.65. The data were taken in 1998-1999 (e-p) and
1999-2000 (e+p) with a center-of-mass energy of 320~GeV and
correspond to an integrated luminosity of 16.4~pb^{-1} and
65.3~pb^{-1} respectively. For Q2 > 1000 GeV2 clear evidence
is observed for an asymmetry between e-p and e+p neutral current
scattering and generalised structure function xF_3$ is
extracted. An extension of analysis to high inelasticity, y=0.75,
allows determination of the longitudinal structure function, F_L, in
the Q2 range from 100<Q^2<800 GeV2. A fit to the charged
current data is used to extract a value for the W boson propagator
mass. The data are found to be in good agreement with Standard Model
predictions.

The QCD description of the small x behaviour of parton distribution
functions in the framework of DGLAP equation, is given. A soft initial
conditions are choosen.
The contributions of twist-two and (renormalon-type) higher-twist
operators of the Wilson operator product expansion are taken into account.
The results are in very good agreement with deep inelastic scattering
experimental data from HERA.

Neutral and charged current deep inelastic scattering cross sections in
e^-p and e^+p scattering have been measured using the ZEUS detector at
HERA. A measurement of the structure function xF_3 has been made by
combining the e^-p neutral current data sample of 16 pb^-1, collected
at a center-of-mass energy of 318 GeV, with the neutral current e^+p
sample of 30 pb^-1, collected at a center-of-mass energy of 300 GeV.
A fit to the charged current e^+p double differential cross-section,
for the data taken at a center-of-mass energy if 300 GeV, has been made
to extract a fit of Mw. New results for the e^+p 40 pb^-1 of neutral
and charged current data, at a center-of-mass energy of 318 GeV, will
be presented.

The analysis is made how the dijet azimuthal correlation in DIS
and real photoproduction at HERA probe the differential (unintegrated)
gluon distribution in the proton. We find a strong dependence
of the azimuthal correlation pattern on Bjorken-x, photon virtuality
and the cut on the jet transverse momenta. A rise of the azimuthal
decorrelation is observed with decreasing Bjorken-x due to the interplay of
perturbative and nonperturbative effects. A strong rise of the same-side jet
rate with photon energy for real photoproduction is predicted.
I discuss conditions for the correlation function to be dominated
by hard perturbative gluons and ways of constraining the size of
the nonperturbative soft component. Some predictions for the THERA
energy range are made. The analysis of the energy dependence of the isolated jet
and two-jet cross sections in photoproduction would be a new way to study
the not yet well constrained unintegrated gluon distributions and
to explore the onset of the pQCD regime. Some further details can be found
in Phys.Lett.B500 (2001) 254-262 (A.Szczurek, N.N.Nikolaev, W Schaefer
and J. Speth).

The evolution of unpolarized parton densities and structure functions
is discussed in massless perturbative QCD. The available partial results
for the three-loop splitting functions are shown to facilitate reliable
next-to-next-to-leading order (NNLO) calculations for a large part of
the kinematical region relevant to the LHC. This allows a considerable
reduction of the theoretical uncertainties of the parton densities.
Corresponding results for the three-loop DIS coefficient functions are
employed to treat the scaling violations of the flavour non-singlet
structure functions up to N^3LO, reducing the theoretical uncertainty
of determinations of alpha_s(M_Z) from these observables to about 1%.
Also presented are estimates of terms of even higher order by Pade
approximations and other methods.

Infrared evolution equations incorporating the running QCD coupling are
constructed and solved for the non-singlet structure functions $f_{NS}$.
Accounting for dropped in DGLAP logs of $x$ leads to a scaling-like small
$x$ behaviour $f_{NS} \sim (\sqrt{Q^2}/x)^a$. In contrast to the leading
logarithmic approximation, intercepts $a$ are numbers and do not
contain $\alpha_s$. It is also shown that the leading
logarithmic approximation may be unreliable for predicting $Q^2$
-dependency of the DIS structure functions at DESY range.

Deep-inelastic positron-proton scattering with initial state photon
radiation (ISR) collected by the HERA experiment H1 is investigated. With
these data the proton structure function F2 is measured, extending the
kinematic reach of the H1 experiment down to four-momentum transfers of
Q2=0.2 GeV2 and intermediate Bjorken-x < 0.0032. The measurements based
on a coherent set of radiative events span from a region (Q2=20 GeV2) in
which perturbative calculations are clearly valid, to a phase space regime
(Q2<1 GeV2) where only phenomenological models can describe the data due
to large influence of non-perturbative effects.

Measurements on the proton structure function F2 published by the HERA
Collaborations H1 and ZEUS at the lowest values of Q^2 are used to
determine the gamma* proton cross section. The data are analysed in
terms of log(1+Q^2/Q_0^2) and extrapolated for Q^2 --> 0 keeping
W^2 fixed. The extrapolated values are compared with the gamma proton
cross section measured by H1 at W=200 Gev and ZEUS at W = 207 GeV.

The dependence of the virtual-photon (gamma^*) structure on the photon
virtuality, Q2, and the average transverse energy of the two highest
transverse energy jets, \bar{E}_T has been studied in the range
10^{-1}<Q^2<10^4 GeV^2. Events were required to have two jets with
transverse energies, E_{T,1}^{\rm jet} > 7.5 GeV and
E_{T,2}^{\rm jet} > 6.5 GeV in the final state using the $k_T$
algorithm in the gamma_* p frame of reference. The cross section in
x_\gamma^{\rm obs}, the fraction of the photon's energy participating
in the production of the two highest transverse energy jets, has been
measured as a function of Q^2 and \bar{E}_T^2. The ratio of the dijet
cross section with x_\gamma^{\rm obs} < 0.75 to that with
x_\gamma^{\rm obs} > 0.75 decreases as Q^2 increases in the three
regions of \bar{E}_T^2 studied. The data are compared with the
predictions of LO pQCD using two different parton distribution
functions of the photon. The measurements can be interpreted in terms
of a resolved photon component that falls with Q^2 and \bar{E}_T^2.

Recent progress is described on estimating the quantitative
uncertainties of parton distribution functions and of the predictions of
quantities that depend on PDFs. The calculations are based on the CTEQ5
global analysis. Two methods have been developed: The Lagrange
Multiplier method for constrained fitting produces optimized PDFs for a
specified value of a quantity of interest; the Hessian method is a
quadratic approximation for which there is a simple master formula for
estimating PDF uncertainty. Applications of these methods to PDF
uncertainties at the Tevatron and LHC colliders are described.

Measurements of inclusive jet differential cross sections in neutral
current DIS have been made in the Breit frame for Q^2 > 125 GeV^2.
Differential inclusive jet cross sections are presented as functions
of jet transverse energy, jet pseudorapidity, jet azimuthal angle and
Q^2. Next-to-leading order QCD calculations have been compared to the
measurements and used to make a precise determination of the strong
coupling constant.

Jet production is studied in the Breit frame in deep-inelastic scattering
with the H1-experiment. The data are compared to the predictions of NLO
QCD calculations. For the determination of alphas a region of phase space
is selected where the NLO corrections are not too large, leading to a
photon virtuality Q^2 > 150 GeV^2 and transverse jet energy E_T,Breit > 7
GeV. The inclusive k_t jet algorithm is found to have the smallest
hadronization corrections.
The jet cross sections depend on alphas and a convolution of matrix
elements, calculable in QCD, and gluon and quark densities of the proton.
Therefore, the first strategy pursued is a simultaneous determination of
alphas and the gluon and quark densities. Besides the jet data, the other
additional information used is the H1 data on the inclusive DIS cross
section. The second strategy is to take the world knowledge of the parton
densities as encoded in the various global parameterizations and fit alphas
only. This results in a competitively precise measurement of the strong
coupling.

Authors: J. Bluemlein, V. Ravindran, J. Ruan, and W. Zhu
We calculate twist--4 coefficient functions for the deep inelastic
structure function $F_2(x,Q^2)$ associated to 4--gluon operator matrix
elements for general values of the Bjorken variable $x$ and study the
numerical effect on the slope $\partial F_2(x,Q^2)/\partial \log Q^2$.
It is shown that these contributions diminish the strongly rising
twist--2 terms towards small values of $x$.

A new and rather stringent criterion is proposed for testing the goodness
of fit between a theory and experiment. It is motivated by the paradox
that the criterion on \chi^2 for testing a theory is much weaker than the
criterion for finding the best fit value of a parameter in the theory. A
method is presented by which the stronger parameter-fitting criterion can
be applied to subsets of data in a global fit. Applications to the CTEQ5
are presented; it is found that there are significant inconsistencies.

Two future neutrino DIS facilities/experiments will be described: a
near-future NuMI experiment using the increased luminosity from a recently
designed/costed new Proton Driver and a future Neutrino Factory based on a
muon storage ring. The important physics accessible with the increased
statistics and improved systematics will be outlined. These topics
include the extraction of parton distribution functions from both nucleon
and nucleus, studies of exclusive states and the use of polarized
targets.

A next-to-leading-order QCD fit was performed on the ZEUS e+p
deep inelastic scattering data, and the gluon and quark densities
of the proton have been extracted. Experimental systematic errors
were considered in this analysis taking into account their
point-to-point correlations, which allows a correct evaluation
of the extracted parton density uncertainties. In addition,
the strong coupling constant, alpha_s, was determined simultaneously.

We report a new measurement of the pseudorapidity (eta)
and transverse-energy (Et) dependence of the inclusive
jet production cross section in pbar p collisions at
sqrt(s) = 1.8 TeV using 95 pb**-1 of data collected with
the DZero detector at the Fermilab Tevatron. The
differential cross section d^2sigma/(dEt deta) is
presented up to |eta| = 3, significantly extending previous
measurements. The results are in good overall agreement with
next-to-leading order predictions from QCD and indicate a
preference for certain parton distribution functions.

Resummed expressions for partonic amplitudes and cross sections
in QCD are affected by the Landau pole singularity. A natural,
gauge-invariant regularization for this singularity is provided by
dimensional continuation, which in simple cases leads to explicit
expressions in terms of analytic functions of the coupling and the
space-time dimension. The method can be applied to finite hard partonic
cross sections, for example to DIS or to the Drell-Yan process, yielding
a correct estimate of the parametric size of power corrections. One abstract covering the two talks:

We present measurements of the semi-inclusive cross-sections for
$\nu_{\mu }$-- and $\bar{\nu}_{\mu }$--nucleon deep inelastic
scattering interactions with two oppositely charged muons in the final
state. These events dominantly arise from production of a charm quark
during the scattering process. The measurement was obtained from the
analysis of 5102 $\nu _{\mu }$-induced and 1458 $\bar{\nu }_{\mu
}$-induced events collected with the NuTeV detector exposed to a
sign-selected beam at the Fermilab Tevatron. We also extract a
cross-section measurement from a re-analysis of 5030 $\nu _{\mu}$-induced
and 1060 $\bar{\nu }_{\mu }$-induced events collected from the
exposure of the same detector to a quad-triplet beam by the CCFR
experiment. The results are combined to obtain the most statistically
precise measurement of neutrino-induced dimuon production
cross-sections to date. These measurements should be of broad use to
phenomenologists interested in the dynamics of charm production, the
strangeness content of the nucleon, and the CKM matrix element
$V_{cd}$.

This year HERA starts operation with polarised lepton
beams at high luminosity. This will permit precision
and exploratory structure function measurements which
are discussed. Deep inelastic scattering can be studied
at much increased energy at THERA when TESLA is built
at DESY. This leads into the saturation region and
explores proton structure at 10^-19m.

  Deep inelastic photon - proton scattering can be discussed both in the
Breit framex and in the proton rest frame (photonic dipole approach).
The latter is particularly suited for describing several features of
diffraction : inclusive diffractive cross section, diffractive jet and
charm production, vector meson exclusive production. In this talk, the
HERA data on these processes are reviewed. They provide informations on
the dipole - proton cross section, which can be used to explore the proton
structure.

A new analysis of CCFR deep inelastic \nu_{\mu}N and \bar{\nu}_{\mu}N
scattering is presented for previously unexplored regions down to
Bjorken x = .0045 and Q^2 = 0.3 GeV^2. Comparisons are made to NMC and
E665 \mu N scattering data and the apparent discrepancy between \mu N
and \nu N scattering in F_2 is addressed in the small Q^2 region.

The present status of the measurements of hadronic structure functions
of the photon, investigated in deep-inelastic electron-photon scattering
at LEP, is presented.
The presentation covers the hadronic structure function F2 of quasi-real
photons as well as the structure function F2eff of virtual photons.
Special emphasis is given to new developments in the analysis and to the
most recent measurements that have been made since the DIS 2000 conference.

I discuss the impact of the most recent data on the MRST global analysis
of structure function and related data - in particular the new jet data
and its implication for the gluon and the effects of new small x structure
function data. In the light of this new data I also consider the
uncertainty in predictions for physical quantities depending on parton
distributions, concentrating on the $W$ cross-section at hadron colliders.

A precise measurement of the inclusive deep-inelastic e+p scattering
cross section is reported in the kinematic range 1.5 < Q^2 < 150 GeV^2
and 3 < 10^(-5) < x < 0.2 The data were recorded with the H1
detector at HERA in 1996 and 1997, and correspond to an integrated
luminosity of 20 pb^(-1).
The gluon momentum distribution is extracted using a NLO QCD fit to
H1 proton structure function data. A fit of the H1 measurements and
high precision mu p data of the BCDMS collaboration determined the
gluon distribution and simultaeneously the strong coupling constant
alpha_s with high experimental precision.

Parametrization of nuclear parton distributions is investigated [1].
The parton distributions are provided at Q^2=1 GeV^2 with a number
of parameters, which are determined by a chi^2 analysis of the data
on nuclear structure functions. Although valence quark distributions
in the medium x region are relatively well determined, the small x
distributions depend slightly on the assumed functional form. It is
difficult to determine the antiquark distributions at medium x and
gluon distributions. From the analysis, we propose parton distribution
functions for nuclei from deuteron to heavy ones. They are provided
either analytical expressions or computer subroutines for practical
usage.
Reference
[1] M. Hirai, S. Kumano, and M. Miyama, hep-ph/0103208.

Results for the production of D*(2010) mesons in
deep-inelastic scattering with the H1 detector at
HERA using an integrated luminosity of 18.6 pb^-1 are
presented. In the kinematic region 1<Q^2<100 GeV^2
and 0.05<y<0.7 an e^+p cross section is measured
for inclusive D* meson production of
8.37+/-0.41(stat)^+1.11_-0.82(sys)^+0.64_-0.39(model) nb
in the visible range 1.5<p_t(D*) GeV, |eta(D*)|<1.5.
Single and double differential inclusive D* meson cross
sections are compared to perturbative QCD calculations
in two different evolution schemes. The charm contribution
to the proton structure, F2^charm(x,Q^2), is determined
by extrapolating the visible charm cross section to the
full phase space.

Charm production has been measured with the ZEUS detector in two
different channels: the D* meson production and the semi-leptonic decay
of the charm. In both cases differential production cross sections have
been measured and compared to NLO QCD predictions.
The charm structure function ($F_2^{c\overline{c}}$) measured by the two
methods is shown, as is the ratio of the charm structure function to the
inclusive structure function ($F_2$).

The latest LEP results on charm production in
collisions of real and virtual photons are reviewed.
Charm events have been identified by leptons from
semileptonic decays, by reconstructing D* and J/psi mesons.
All current data on the total inclusive charm cross section
are shown and compared with theoretical predictions.
Production cross-section as a function of the two photon
centre-of-mass energy are also presented and compared with
NLO QCD predictions.

Phenomenological studies of the proton structure function
F2, measured in e+p scattering using the ZEUS detector at HERA, are presented.
Particular emphasis is placed on the transition from hadronic type
behavior at Q2 \approx 0 to the deep inelastic scattering regime (Q2>>1 GeV^2).
The derivatives dln(F2)/dln(1/x) for fixed Q2 and dF2/dlog(Q2) for fixed x
are shown, and a comparison of the data to several models is made.

   New physics" phenomena are looked for in high Q2 NC DIS data
   collected by H1 and ZEUS in 1994-2000. Contact Interaction
   approximation is used to compare data with predictions of different
   models. Limits are set on mass scale parameters in compositeness
   models, model of Large Extra DImensions and leptoquark models.