Computational learning theory is one of the first attempts to construct a mathematical theory of a cognitive process. It has been a field of much interest and rapid growth in recent years. This text provides a framework for studying a variety of algorithmic processes, such as those currently in use for training artificial neural networks. The authors concentrate on an approximate model for learning and gradually develop the ideas of efficiency considerations. Finally, they consider applications of the theory to artificial neural networks. An abundance of exercises and an extensive list of references round out the text. This volume provides a comprehensive review of the topic, including information drawn from logic, probability, and complexity theory. It forms a solid introduction to the theory of comptutational learning suitable for a broad spectrum of graduate students from theoretical computer science to mathematics.