The Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C() and L(X), for a compact Hausdorff space and X a -finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.