Description Factorized S Matrices and Lattice Statistical Systems – A. B. Zamolodchikov was first published in 1980 in the series Soviet Scientific Reviews/Physics Reviews edited by I. M. Khalatnikov: Volume 2: a compiled volume. This classic paper studies the general characteristics of relativistic factorized S-matrices in two dimensional space-time. It shows that for Euclidean values of external momenta, multiparticle elements in such S matrices formally define special model systems of lattice – statistics model systems ( S models) that have a number of characteristics in common with the Baxter eight-vertex model Contents Include Introduction Factorized S Matrices Conservation laws and factorization General structure of the relativistic factorized S matrix Symmetries and analytical properties of the two particle S matrix (two-particle unitarity) Algebraic representation of the factorization S matrix Some general characteristics of solutions for the equations of factorization, analyticity and unitarity, Z-Invarient Models of Lattice Statistics Eight-Vertex Baxter model Factorized S matrices as Z-invariant lattice systems Factorization of the partition function In the course of the last thirty years these ideas and concepts have been developed and applied extensively in theoretical physics and the republication of this classic paper provides an accessible reference text for students and researchers