This book provides an extensive introduction to recent progress in the theory of locally finite groups, algebraic groups, and finite groups of Lie type. Fifteen specialists in the field have written survey articles covering the major themes of the subject, such as the theory of simple locally finite groups and the theory of finitary linear groups. The articles are based on lectures given at the highly successful NATO ASI held in Istanbul in August 1994 and organized by the late Brian Hartley. The book which is accessible to graduate students and others with limited specialist knowledge, reaches the frontiers of current research in this rapidly developing area. Most of the main results of the subject are stated and discussed, including results not yet published elsewhere and a number of open problems are formulated which are likely to stimulate future research. The book will thus be of great interest to all research workers in group theory.