In the last decade, the subject of nonsmooth analysis has grown rapidly, due to the recognition that nondifferentiable phenomena are more widespread and more fundamental to applications than had been thought. In recent years, it has come to play a role in functional analysis, optimization, differential equations, optimal design, mechanics and plasticity, control theory, and, increasingly, in analysis generally. This volume presents the essentials of the subject clearly and succinctly, together with some of its applications and a generous supply of interesting exercise. A short course on mathematical control theory, founded on the material of the earlier chapters, appears at the end of the volume. End-of-chapter problems supplement the in-text exercises.