The first result in the theory of centralizers in associative rings was published at the begining of the 1990s. This advanced algebra book is the first one on this subject . Authors have obtained nice results on centralizers. Also,there have been results dealing with different kinds of algebraic conditions that force additive mappings on rings to be centralizers. This book has five chapters. Chapter one focuses on mentioning the preliminaries that are used throughout the book. Chapter two displays the results concerning ordinary centralizers.Chapter three deals with theta - centralizers. Chapter four discusses centralizers in rings with involution. Chapters two, three and four are considered as a survey of the results appearing in the literature equipped with brief sketches of proofs. Thus, the reader may be lightened through a few steps into the original proofs. Chapter five presents the results that we have obtained during the preparation of the book .