This book provides a complete presentation of nonsmooth critical point theory. It collects together tools and results from nonsmooth analysis into a systematic survey of advances that have been made by many people working in the field since the early 1980s. After offering a comprehensive treatment of nonsmooth critical point theory, the authors study nonlinear second order boundary value problems both for ODEs (Chapter 3) and elliptic equations (Chapter 4). They do not limit themselves to problems in variational form, also studying in detail equations driven by the p-Laplacian, its generalizations and their special properties, considering a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book and a rich bibliography forms a guide to the relevant literature. The book can be recommended to all readers interested in nonlinear analysis and also as a reference book.