This book provides a comprehensive introduction to the theory of magnetic field line reconnection, now a major subject in plasma physics. The book focuses on the various reconnection mechanisms dominating magnetic processes under the different plasma conditions encountered in astrophysical systems and in laboratory fusion devices. The book consists of two major parts: the first deals with the classical resistive approach, while the second presents an overview of weakly collisional or collisionless plasmas. Applications primarily concern astrophysical phenomena and dynamo theory, with emphasis on the solar and geodynamo, as well as magnetospheric substorms, the most spectacular reconnection events in the magnetospheric plasma. The theoretical procedures and results also apply directly to reconnection processes in laboratory plasmas, in particular the sawtooth phenomenon in tokamaks. The book will be of value to graduate students and researchers interested in magnetic processes both in astrophysical and laboratory plasma physics.