This original work presents up-to-date information on three major topics in mathematics research: the theory of weak convergence of convolution products of probability measures in semigroups; the theory of random walks with values in semigroups; and the applications of these theories to products of random matrices. The authors introduce the main topics through the fundamentals of abstract semigroup theory and significant research results concerning its application to concrete semigroups of matrices.

The material is suitable for a two-semester graduate course on weak convergence and random walks. It is assumed that the student will have a background in Probability Theory, Measure Theory, and Group Theory.