The field of differential topology underwent a dramatic development period between 1955 and 1965. This collection of articles written by one of the creators of this field contains not only original papers, but also previously unpublished expository lectures. It includes commentary by the author, filling in some of the historical context, and outlining subsequent developments. It includes a rich bibliography of newer and older papers, providing a wider and deeper understanding of the subject. It also outlines the actual state of the art, and provides an index that will allow the reader to browse easily through the book. Of particular interest are the articles related to the existence of exotic differentiable structures on spheres, the achievement for which J. Milnor was awarded the Fields Medal in 1962.