This second edition offers a wide-ranging update and revision of the
previous edition. The updated chapters represent new insights in
averaging, in particular its relation with dynamical systems and the
theory of normal forms. Also new are survey appendices on invariant
manifolds. Since the first edition, the book has expanded in length and
a third author, James Murdock has been added. One of the most striking
features of the book is the collection of examples, which range from the
very simple to some that are elaborate, realistic, and of considerable
practical importance. Most of them are presented in careful detail and
are illustrated with profuse, illuminating diagrams.