The discipline of nonlinear dynamics has developed explosively in all areas of physics. This comprehensive primer, first published in 2006, summarizes the main developments in the mathematical theory of dynamical systems, chaos, pattern formation and complexity. An introduction to mathematical concepts and techniques is given in the first part of the book, before being applied to stellar, interstellar, galactic and large scale complex phenomena in the Universe. Regev demonstrates the possible application of ideas including strange attractors, Poincare sections, fractals, bifurcations, and complex spatial patterns, to specific astrophysical problems. This self-contained text will appeal to a broad audience of astrophysicists and astronomers who wish to understand and apply modern dynamical approaches to the problems they are working on. It provides researchers and graduate students with the investigative tools they need to fully explore chaotic and complex phenomena.