This book is an in-depth and broad text on the subject of chaos in dynamical systems. It is intended to serve both as a graduate course text for science and engineering students, and as a reference and introduction to the subject for researchers. Within the past decade scientists, mathematicians and engineers have realized that a large variety of systems exhibit complicated evolution with time. This complicated behaviour, called chaos, occurs so frequently that it has become important for workers in many disciplines to have a good grasp of the fundamentals and basic tools of the emerging science of chaotic dynamics. The author's style is pedagogic, and the book will be of value both as a graduate text and also as a reference work for researchers in science and engineering needing to understand this important new subject. Homework problems are also included throughout the book.