Integral transforms are used throughout mathematics, science, and engineering disciplines. This book outlines a systematic treatment of the theory and methods of the subject, presenting techniques used to solve a variety of physical problems. This edition features chapters on fractional calculus and applications of Laplace transforms to fractional differential equations. It also includes material and applications from areas such as dynamical systems, wave propagation, quantum mechanics, and heat conduction. Useful both as a textbook and a reference, this edition includes additional problem sets and updated exercises in each chapter.