Although chaotic dynamics had been known to exist for a long time, its importance for a broad variety of applications began to be widely appreciated only within the last decade or so. Concurrently, there has been enormous interest both within the mathematical community and among engineers and scientists. The field continues to develop rapidly in many directions, and its implications continue to grow. Naturally, such a situation calls for textbooks to serve the need of providing courses to students who will eventually utilize concepts of chaotic dynamics in their future careers. A variety of chaos texts now exists. In my teaching of several courses on chaos, however, I found that the existing texts were not altogether suitable for the type of course I was giving, with respect to both level and coverage of topics. Hence I was motivated to prepare and circulate notes for my class, and these notes led to this book. The book is intended for use in a graduate course for scientists and engineers. Accordingly, any mathematical concepts that such readers may not be familiar with (e.g., measure, Cantor sets, etc.) are introduced and informally explained as needed. While the intended readers are not mathematicians, there is a greater emphasis on basic mathematical concepts than in most other books that address the same audience. The style is pedagogical, and it is hoped that the very interesting, sometimes difficult, concepts that are the backbone for studies of chaos are made clear.