Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering by Steven H. Strogatz

Excellent mathematical introduction to the dynamics of non-linear systems. The text style is rather informal, and very clear, and many of the concepts and results presented are exposed in an intuitive way. Beginning from uni-dimensional systems and reaching to chaos and strange attractors, there’s that typical progressive crescendo in complexity which makes the reading worth and sticking. The book also contains a lot of examples taken from several disciplines (physics, chemistry, population dynamics, biology, and so on) and many exercises at the end of chapters.
Highly recommended.