The scope of this research algebra book is intended for a highly completed knowledge in the topic of commutativity of associative rings with ordinary derivations. The study of this theme has been begun in 1957 by Posner and has been followed by many authors through studying different algebraic conditions. This book contains six chapters. Chapter one is devoted to review briefly the terminology and the technical language that are basic to the understanding of the book. Chapter two deals with second classical theorem of Posner on prime rings with derivations and its diverse generalizations. Chapter three concerns with the commutativity of prime and semiprime rings endowed with derivations, begining with a classical result due to Herstein on derivations in prime rings. Chapter four focuses on the study of the commutativity of prime rings with involution. Chapter five concerns with commutativity in semiprime rings admitting derivations, starting with classical theorems of Daif and Bell. Chapter six presents new results that have been obtained during the preparation of the book.