This volume, starts with the concept of C-group for any category C (with products and final object), but the author's do not exploit it in its full generality. The book is meant to be introductory to the theory, and therefore the necessary background to its minimum possible level is minimised.

Dieudonne Jean A. University de Nice Sophia-Antipolis France

Foreword, Notations, Chapter I DEFINITION OF FORMAL GROUPS, Chapter II INFINITESIMAL FORMAL GROUPS, Chapter III INFINITESIMAL COMMUTATIVE GROUPS, Chapter IV REPRESENTABLE REDUCED INFINITESIMAL GROUPS, Bibliography, Index