By now, there are also many physics textbooks on ``chaos''. Most lack depth, and many of them are plain bad, emphasizing pictorial and computer-graphics aspects of dynamics and short changing the student on the theory. That's a pity, as the subject in its beauty and intellectual depth ranks alongside statistical mechanics and quantum field theory, with which it shares many fundamental techniques. The book represents authors' attempt to formulate the subject as one of the basic cornerstones of the advanced graduate physics curriculum of future.