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.

The cross section for dijet photoproduction at high transverse energies is presented as a function of the transverse energies and the pseudorapidities of the jets. The measurement is performed using a sample of ep-interactions corresponding to an integrated luminosity of 6.3 pb^(-1), recorded by the ZEUS detector.Jets are defined by applying a k_T-clustering algorithm to the hadrons observed in the final state. The measured cross sections are compared to next-to-leading order QCD calculations. In a kinematic regime where theoretical uncertainties are expected to be small, the measured cross sections are higher than these calculations.

First inclusive measurements of isolated prompt photons in photoproduction at the HERA ep collider have been made with the ZEUS detector, using an integrated luminosity of 38.4 pb$^{-1}$. Cross sections are given as a function of the pseudorapidity and the transverse energy ($\eta^\gamma$, \eTg) of the photon, for $\eTg > $ 5 GeV in the $\gamma p$ centre-of-mass energy range 134-285 GeV. Comparisons are made with predictions from Monte Carlo models having leading-logarithm parton showers, and with next-to-leading-order QCD calculations, using currently available parameterisations of the photon structure. For forward $\eta^\gamma$ (proton direction) good agreement is found, but in the rear direction all predictions fall below the data.

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.

Inclusive dijet and trijet production in deep inelastic $ep$ scattering has been measured for $10&lt;Q^2&lt;100$ GeV$^2$ and low Bjorken $x$, $10^{-4}&lt;x_{\rm Bj}&lt;10^{-2}$. The data were taken at the HERA $ep$ collider with centre-of-mass energy $\sqrt{s} = 318 \gev$ using the ZEUS detector and correspond to an integrated luminosity of $82 {\rm pb}^{-1}$. Jets were identified in the hadronic centre-of-mass (HCM) frame using the $k_{T}$ cluster algorithm in the longitudinally invariant inclusive mode. Measurements of dijet and trijet differential cross sections are presented as functions of $Q^2$, $x_{\rm Bj}$, jet transverse energy, and jet pseudorapidity. As a further examination of low-$x_{\rm Bj}$ dynamics, multi-differential cross sections as functions of the jet correlations in transverse momenta, azimuthal angles, and pseudorapidity are also presented. Calculations at $\mathcal{O}(\alpha_{s}^3)$ generally describe the trijet data well and improve the description of the dijet data compared to the calculation at $\mathcal{O}(\alpha_{s}^2)$.

Multijet production rates in neutral current deep inelastic scattering have been measured in the range of exchanged boson virtualities 10 < Q2 < 5000 GeV2. The data were taken at the ep collider HERA with centre-of-mass energy sqrt(s) = 318 GeV using the ZEUS detector and correspond to an integrated luminosity of 82.2 pb-1. Jets were identified in the Breit frame using the k_T cluster algorithm in the longitudinally invariant inclusive mode. Measurements of differential dijet and trijet cross sections are presented as functions of jet transverse energy E_{T,B}{jet}, pseudorapidity eta_{LAB}{jet} and Q2 with E_{T,B}{jet} > 5 GeV and -1 < eta_{LAB}{jet} < 2.5. Next-to-leading-order QCD calculations describe the data well. The value of the strong coupling constant alpha_s(M_Z), determined from the ratio of the trijet to dijet cross sections, is alpha_s(M_Z) = 0.1179 pm 0.0013(stat.) {+0.0028}_{-0.0046}(exp.) {+0.0064}_{-0.0046}(th.)

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.

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.

Differential cross sections for dijet photoproduction in association with a leading neutron using the reaction e^+ + p --> e^+ + n + jet + jet + X_r have been measured with the ZEUS detector at HERA using an integrated luminosity of 6.4 pb^{-1}. The fraction of dijet events with a leading neutron in the final state was studied as a function of the jet kinematic variables. The cross sections were measured for jet transverse energies E^{jet}_T > 6 GeV, neutron energy E_n > 400 GeV, and neutron production angle theta_n < 0.8 mrad. The data are broadly consistent with factorization of the lepton and hadron vertices and with a simple one-pion-exchange model.

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.).