This book contains a collection of 28 contributions on the topics of bifurcation theory and dynamical systems, mostly from the point of view of symmetry breaking, which has been revealed to be a powerful tool in the understanding of pattern formation and in the scientific application of these theories. It includes a number of results which have not been previously made available in book form. Computational aspects of these theories are also considered. For graduate and postgraduate students of nonlinear applied mathematics, as well as any scientist or engineer interested in pattern formation and nonlinear instabilities.