The precision Monte Carlo event generator KK for two-fermion final states in $e^+ e^-$ collisions. We present the Monte Carlo event generator 𝒦𝒦 version 4.13 for precision predictions of the electroweak standard model for the process e + e - →ff ¯+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).