This is the third, substantially revised edition of this important monograph. The book is concerned with Kac–Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.

‘A clear account of Kac–Moody algebras by one of the founders … Eminently suitable as an introduction … with a surprising number of exercises.’

Source: American Mathematical Monthly

‘ … a useful contribution. All the basic elements of the subject are covered … Many results which were previously scattered about in the literature are collected here … The book also contains many exercises and useful comments …’

Source: Physics in Canada