The algebraic Bethe ansatz is one of the main approaches to solving integrable models in statistical mechanics. Although many publications consider this important topic most assume a substantial prior knowledge on the part of the reader. This book however provides a detailed introduction to aspects of algebraic Bethe ansatz without assuming any prior knowledge of the subject matter. It is an ideal companion to any mathematics student or researcher seeking to advance their understanding of this fascinating area of statistical mechanics. In particular the book fully explains all preliminaries in the context of the 8- vertex model including the solution of the Yang- Baxter equations and also considers the special case of the 6-vertex model in both the homogeneous and inhomogeneous cases.