We present a detailed analysis of the rishon model of composite quarks, leptons, scalar particles and weak bosons. The fundamental lagrangian is assumed to be gauge invariant under SU(3) H × SU(3) C × U(1) EM. The fundamental particles are the two types of rishons (T and V), hypergluons, gluons and the photon. No fundamental scalars exist. Below the hypercolor scale Λ H, only SU(3) H singlets exist. The simplest composite fermions are made of three rishons or three antirishons and reproduce the observed properties of one generation of quarks and leptons. A new approximate SU(2) L × SU(2) R ×U(1) B− L symmetry emerges at the composite level. The weak interactions appear only at the composite level as residual short-range interactions among hypercolor singlets. If composite W and Z bosons are formed, the effective lagrangian at low energies is likely to be gauge invariant and renormalizable, except for terms proportional to inverse powers of Λ H. Two elusive Goldstone bosons are predicted by the model. The 't Hooft consistency requirement is simply obeyed in a manner similar to the situation in QCD. The generation problem and the proton's decay as well as some theoretical difficulties and experimental signatures are briefly discussed. Two main difficulties are noted: an unusual pattern of chiral symmetry breaking and the existence of light composite vector bosons.