This book deals with a series of topics on the cutting edge of nonlinear science, striking a balance between theory and experiment. It consists of two innovative introductory presentations on dynamical systems and fluid dynamics and six chapters on advanced research. A nontrivial interrelation between the different topics becomes apparent throughout the book as an indication of the underlying unity and genericity of nonlinear phenomena. There is a continuous emphasis on conceptual issues often introduced via concrete examples. A common feature is that most of the systems under study are extended, nonhomogeneous and far from equilibrium. The book also exhibits an interesting interplay between deterministic and stochastic approaches.