Single- and double-differential inclusive dijet cross sections in neutral current deep inelastic ep scattering have been measured with the ZEUS detector using an integrated luminosity of 374 pb^-1. The measurement was performed at large values of the photon virtuality, Q^2, between 125 and 20000 GeV^2. The jets were reconstructed with the k_T cluster algorithm in the Breit reference frame and selected by requiring their transverse energies in the Breit frame, E_T,B^jet, to be larger than 8 GeV. In addition, the invariant mass of the dijet system, M_jj, was required to be greater than 20 GeV. The cross sections are described by the predictions of next-to-leading-order QCD.

Deep inelastic scattering and its diffractive component, $ep \to e^{\prime}\gamma^* p \to e^{\prime}XN$, have been studied at HERA with the ZEUS detector using an integrated luminosity of 52.4 pb$^{-1}$. The $M_X$ method has been used to extract the diffractive contribution. A wide range in the centre-of-mass energy $W$ (37 -- 245 GeV), photon virtuality $Q^2$ (20 -- 450 GeV$^2$) and mass $M_X$ (0.28 -- 35 GeV) is covered. The diffractive cross section for $2 < M_X < 15$ GeV rises strongly with $W$, the rise becoming steeper as $Q^2$ increases. The data are also presented in terms of the diffractive structure function, $F^{\rm D(3)}_2$, of the proton. For fixed $Q^2$ and fixed $M_X$, $\xpom F^{\rm D(3)}_2$ shows a strong rise as $\xpom \to 0$, where $\xpom$ is the fraction of the proton momentum carried by the Pomeron. For Bjorken-$x < 1 \cdot 10^{-3}$, $\xpom F^{\rm D(3)}_2$ shows positive $\log Q^2$ scaling violations, while for $x \ge 5 \cdot 10^{-3}$ negative scaling violations are observed. The diffractive structure function is compatible with being leading twist. The data show that Regge factorisation is broken.

Jet cross sections were measured in charged current deep inelastic e+-p scattering at high boson virtualities Q^2 with the ZEUS detector at HERA II using an integrated luminosity of 0.36 fb^-1. Differential cross sections are presented for inclusive-jet production as functions of Q^2, Bjorken x and the jet transverse energy and pseudorapidity. The dijet invariant mass cross section is also presented. Observation of three- and four-jet events in charged-current e+-p processes is reported for the first time. The predictions of next-to-leading-order (NLO) QCD calculations are compared to the measurements. The measured inclusive-jet cross sections are well described in shape and normalization by the NLO predictions. The data have the potential to constrain the u and d valence quark distributions in the proton if included as input to global fits.

Three- and four-jet final states have been measured in photoproduction at HERA using the ZEUS detector with an integrated luminosity of 121 pb^-1. The results are presented for jets with transverse energy E_T^jet>6 GeV and pseudorapidity |eta^jet|<2.4, in the kinematic region given by the virtuality of the photon Q^2<1 GeV^2 and the inelasticity 0.2<y<0.85 and in two mass regions defined as 25<M_nj<50 GeV and M_nj>50 GeV, where M_nj is the invariant mass of the n-jet system. The four-jet photoproduction cross section has been measured for the first time and represents the highest-order process studied at HERA. Both the three- and four-jet cross sections have been compared with leading-logarithmic parton-shower Monte Carlo models, with and without multi-parton interactions. The three-jet cross sections have been compared to an order(alpha alpha_s^2) perturbative QCD calculation.

Inclusive D* production is measured in deep-inelastic ep scattering at HERA with the H1 detector. In addition, the production of dijets in events with a D* meson is investigated. The analysis covers values of photon virtuality 2< Q^2 <=100 GeV^2 and of inelasticity 0.05<= y <= 0.7. Differential cross sections are measured as a function of Q^2 and x and of various D* meson and jet observables. Within the experimental and theoretical uncertainties all measured cross sections are found to be adequately described by next-to-leading order (NLO) QCD calculations, based on the photon-gluon fusion process and DGLAP evolution, without the need for an additional resolved component of the photon beyond what is included at NLO. A reasonable description of the data is also achieved by a prediction based on the CCFM evolution of partons involving the k_T-unintegrated gluon distribution of the proton.

Inclusive jet cross sections in photoproduction for events containing a $D^*$ meson have been measured with the ZEUS detector at HERA using an integrated luminosity of $78.6 {\rm pb}^{-1}$. The events were required to have a virtuality of the incoming photon, $Q^2$, of less than 1 GeV$^2$, and a photon-proton centre-of-mass energy in the range $130&lt;W_{\gamma p}&lt;280 {\rm GeV}$. The measurements are compared with next-to-leading-order (NLO) QCD calculations. Good agreement is found with the NLO calculations over most of the measured kinematic region. Requiring a second jet in the event allowed a more detailed comparison with QCD calculations. The measured dijet cross sections are also compared to Monte Carlo (MC) models which incorporate leading-order matrix elements followed by parton showers and hadronisation. The NLO QCD predictions are in general agreement with the data although differences have been isolated to regions where contributions from higher orders are expected to be significant. The MC models give a better description than the NLO predictions of the shape of the measured cross sections.

Deep inelastic scattering and its diffractive component, ep -> e'gamma*p ->e'XN, have been studied at HERA with the ZEUS detector using an integrated luminosity of 4.2 pb-1. The measurement covers a wide range in the gamma*p c.m. energy W (37 - 245 GeV), photon virtuality Q2 (2.2 - 80 GeV2) and mass Mx. The diffractive cross section for Mx > 2 GeV rises strongly with W: the rise is steeper with increasing Q2. The latter observation excludes the description of diffractive deep inelastic scattering in terms of the exchange of a single Pomeron. The ratio of diffractive to total cross section is constant as a function of W, in contradiction to the expectation of Regge phenomenology combined with a naive extension of the optical theorem to gamma*p scattering. Above Mx of 8 GeV, the ratio is flat with Q2, indicating a leading-twist behaviour of the diffractive cross section. The data are also presented in terms of the diffractive structure function, F2D(3)(beta,xpom,Q2), of the proton. For fixed beta, the Q2 dependence of xpom F2D(3) changes with xpom in violation of Regge factorisation. For fixed xpom, xpom F2D(3) rises as beta -> 0, the rise accelerating with increasing Q2. These positive scaling violations suggest substantial contributions of perturbative effects in the diffractive DIS cross section.

Jet substructure and differential cross sections for jets produced in the photoproduction and deep inelastic ep scattering regimes have been measured with the ZEUS detector at HERA using an integrated luminosity of 82.2 pb-1. The substructure of jets has been studied in terms of the jet shape and subjet multiplicity for jets with transverse energies Et(jet) > 17 GeV. The data are well described by the QCD calculations. The jet shape and subjet multiplicity are used to tag gluon- and quark-initiated jets. Jet cross sections as functions of Et(jet), jet pseudorapidity, the jet-jet scattering angle, dijet invariant mass and the fraction of the photon energy carried by the dijet system are presented for gluon- and quark-tagged jets. The data exhibit the behaviour expected from the underlying parton dynamics. A value of alphas(Mz) of alphas(Mz) = 0.1176 +-0.0009(stat.) -0.0026 +0.0009 (exp.) -0.0072 +0.0091 (th.) was extracted from the measurements of jet shapes in deep inelastic scattering.

Dijet cross sections as functions of several jet observables are measured in photoproduction using the H1 detector at HERA. The data sample comprises e^+p data with an integrated luminosity of 34.9 pb^(-1). Jets are selected using the inclusive k_T algorithm with a minimum transverse energy of 25 GeV for the leading jet. The phase space covers longitudinal proton momentum fraction x_p and photon longitudinal momentum fraction x_gamma in the ranges 0.05<x_p<0.6 and 0.1<x_gamma<1. The predictions of next-to-leading order perturbative QCD, including recent photon and proton parton densities, are found to be compatible with the data in a wide kinematical range.

Three-jet production is studied for the first time in deep-inelastic positron-proton scattering. The measurement carried out with the H1 detector at HERA covers a large range of four-momentum transfer squared 5 < Q^2 < 5000 GeV^2 and invariant three-jet masses 25 < M_(3jet) < 140 GeV. Jets are defined by the inclusive k_T algorithm in the Breit frame. The size of the three-jet cross section and the ratio of the three-jet to the dijet cross section R_(3/2) are described over the whole phase space by the predictions of perturbative QCD in next-to-leading order. The shapes of angular jet distributions deviate significantly from a uniform population of the available phase space but are well described by the QCD calculation.

Dijet production has been studied in neutral current deep inelastic e+p scattering for 470 < Q**2 < 20000 GeV**2 with the ZEUS detector at HERA using an integrated luminosity of 38.4 pb**{-1}. Dijet differential cross sections are presented in a kinematic region where both theoretical and experimental uncertainties are small. Next-to-leading-order (NLO) QCD calculations describe the measured differential cross sections well. A QCD analysis of the measured dijet fraction as a function of Q**2 allows both a precise determination of alpha_s(M_Z) and a test of the energy-scale dependence of the strong coupling constant. A detailed analysis provides an improved estimate of the uncertainties of the NLO QCD cross sections arising from the parton distribution functions of the proton. The value of alpha_s(M_Z), as determined from the QCD fit, is alpha_s(M_Z) = 0.1166 +- 0.0019 (stat.) {+ 0.0024}_{-0.0033} (exp.)} {+ 0.0057}_{- 0.0044} (th.).

Jet production in charged and neutral current events in the kinematic range of Q^2 from 640 to 35000 GeV^2 is studied in deep-inelastic positron-proton scattering at HERA. The measured rate of multi-jet events and distributions of jet polar angle, transverse energy, dijet mass, and other dijet variables are presented. Using parton densities derived from inclusive DIS cross sections, perturbative QCD calculations in NLO are found to give a consistent description of both the neutral and charged current dijet production. A direct, model independent comparison of the jet distributions in charged and neutral current events confirms that the QCD dynamics of the hadronic final state is independent of the underlying electroweak scattering process.

Differential dijet cross sections have been measured with the ZEUS detector for photoproduction events in which the hadronic final state containing the jets is separated with respect to the outgoing proton direction by a large rapidity gap. The cross section has been measured as a function of the fraction of the photon (x_gamma^OBS) and pomeron (beta^OBS) momentum participating in the production of the dijet system. The observed x_gamma^OBS dependence shows evidence for the presence of a resolved- as well as a direct-photon component. The measured cross section d(sigma)/d(beta^OBS) increases as beta^OBS increases indicating that there is a sizeable contribution to dijet production from those events in which a large fraction of the pomeron momentum participates in the hard scattering. These cross sections and the ZEUS measurements of the diffractive structure function can be described by calculations based on parton densities in the pomeron which evolve according to the QCD evolution equations and include a substantial hard momentum component of gluons in the pomeron.