Hadron multiplicities

(QCD) are summarized. The QCD equations for the generating functions of the multiplicity distributions are presented both for fixed and running coupli ng strengths. The mean multiplicities of gluon and quark jets, their ratio, higher moments, and the slopes of multiplicities as a function of energy s cale, are among the main global features of multiplicity for which QCD resu lts exist. Recent data from high energy e(+)e(-) experiments, including res ults for separated quark and gluon jets, allow rather direct tests of these results. The theoretical predictions are generally quite successful when c onfronted with data. Jet and subjet multiplicities are described. Multiplic ity in limited regions of phase space is discussed in the context of interm ittency and fractality. The problem of singularities in the generating func tions is formulated. Some special features of average multiplicities in hea vy quark jets are described. (C) 2001 Elsevier Science B.V. All rights rese rved.