Within nonlinear spatio-temporal dynamics, active lattice systems are of relevance to the study of multi-dimensional dynamical systems and the theory of nonlinear waves and dis- sipative structures of extended systems. In this book, the authors deal with basic concepts and models, with methodolo- gies for studying the existence and stability of motions, understanding the mechanisms of formation of patterns and waves, their propagation and interactions in active lattice systems, and about how much cooperation or competition bet- ween order and chaos is crucial for synergetic behavior and evolution. The results described in the book have both inter- and trans-disciplinary features and a fundamental character. It is a textbook for graduate courses in nonlinear sciences, including physics, biophysics, biomathematics, bioengineering, neurodynamics, electrical and electronic engineering, mathematical economics, and computer sciences.