Nonsmooth Analysis is a relatively recent area of mathematical analysis. The literature about this subject consists mainly in research papers and books. The purpose of this book is to provide a handbook for undergraduate and graduate students of mathematics that introduce this interesting area in detail.<ul><li>Includes different kinds of sub and super differentials as well as generalized gradients</li><li>Includes also the main tools of the theory, as Sum and Chain Rules or Mean Value theorems</li><li>Content is introduced in an elementary way, developing many examples, allowing the reader to understand a theory which is scattered in many papers and research books</li></ul>