Contents:

• Introduction
• Transfer Matrices: On Commuting Transfer Matrices
• On Exactly Solved Cases
• Algebra: General Principles
• Temperley-Lieb Algebra: Generic Cases
• Special Cases
• Graph Temperley-Lieb Algebras
• Hecke Algebras
• Algebraic Formalism for Z_Q Symmetry
• The Modelling of Phase Transitions
• Vertex Models and Related Algebras, Braids and Cables

"This is an excellent survey of the Potts model and related matters in statistical mechanics. The first chapter constitutes a good introduction to statistical mechanics with a discussion of modelling principles, partition functions and Hamiltonians, lattices, statistical mechanics functions such as free energy. There are good general discussions of phase transitions, order parameters and critical exponents. Then the Potts models are defined and related to dichromatic polynomials and to the special case of the Ising model. The chapter ends with a discussion of block spin renormalization ... This book is a fine source of basic results about the Potts model and its mathematical physics environment."