This book provides a self-contained introductory course on dynamical systems for advanced undergraduate students as well as a selection of recent developments in dynamical systems that serve to illustrate applications and refinements of the ideas from this course. The parts differ fundamentally in pedagogical approach but are closely interrelated. Either part can stand on its own; the course is complete without the panorama, and the panorama does not require this specific course as background. Scientists and engineers may use this book by picking and choosing, from both the panorama and the course text. Errata and other pertinent information can be found by visiting the first author's web page.

Introduction. The book begins with an introduction to pique interest in dynamics and to present samples of what scientific and mathematical problems dynamics can address. It adds motivation to the course but it is not a required part of it.

The Course. The undergraduate course assumes only knowledge about linear maps and eigenvalues, multivariable differential calculus, and Riemann integration with proofs. Some background is developed in Chapter 9 and the Appendix. Occasionally somewhat more involved portions of the text are set off with this different font to emphasize that the course will remain self-contained when these are omitted. These portions do not assume any more prior knowledge. Dynamics provides the concepts and tools to describe and understand complex long-term behavior in systems that evolve in time. The course accordingly develops these ideas in a gradual progression toward ever greater complexity, with proofs. Both topological and statistical points of view are developed. We know of no other text that makes both accessible at the undergraduate level.