We present the Monte Carlo event generator KK version 4.13 for precision predictions of the Electroweak Standard Model for the process e +e -→f f̄+nγ , f=μ,τ,d,u,s,c,b , at centre-of-mass energies from τ lepton threshold to 1 TeV, that is for LEP, SLC, future Linear Colliders, b,c,τ -factories, etc. Effects due to photon emission from initial beams and outgoing fermions are calculated in QED up to second order, including all interference effects, within Coherent Exclusive Exponentiation (CEEX), which is based on Yennie-Frautschi-Suura exponentiation. Electroweak corrections are included in first order, with higher-order extensions, using the DIZET 6.21 library. Final-state quarks hadronize according to the parton shower model using JETSET. Beams can be polarized longitudinally and transversely. Decay of the τ leptons is simulated using the TAUOLA library, taking into account spin polarization effects as well. In particular the complete spin correlations density matrix of the initial-state beams and final state τ 's is incorporated in an exact manner. Effects due to beamstrahlung are simulated in a realistic way. The main improvements with respect to KORALZ are: (a) inclusion of the initial-final state QED interference, (b) inclusion of the exact matrix element for two photons, and (c) inclusion of the transverse spin correlations in τ decays (as in KORALB).