This is first modern treatment of orthogonal polynomials from the viewpoint of special functions. The coverage is encyclopaedic, including classical topics such as Jacobi, Hermite, Laguerre, Hahn, Charlier and Meixner polynomials as well as those (e.g. Askey-Wilson and Al-Salam - Chihara polynomial systems) discovered over the last 50 years: multiple orthogonal polynomials are dicussed for the first time in book form. Many modern applications of the subject are dealt with, including birth- and death- processes, integrable systems, combinatorics, and physical models. A chapter on open research problems and conjectures is designed to stimulate further research on the subject. Exercises of varying degrees of difficulty are included to help the graduate student and the newcomer. A comprehensive bibliography rounds off the work, which will be valued as an authoritative reference and for graduate teaching, in which role it has already been successfully class-tested.

• A comprehensive coverage of all the orthogonal polynomials discovered in the last fifty years, as well as classical work, and a complete chapter devoted to open problems and conjectures

• Contains a chapter on multiple orthogonal polynomials, a first in book form

• Contains applications of the subject to such areas as birth- and death-processes, integrable systems, combinatorics, and physical models