This text 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. Computational aspects of these theories are also considered. It is designed for graduate and postgraduate students of nonlinear applied mathematics, as well as any scientist or engineer interested in pattern formation and nonlinear instabilities. Dynamical systems and bifurcation theory are mathematical tools which are suitable for the study of time evolution and changes in the physical world. The introduction of the concept of symmetry and symmetry breaking in the theories enlarges their spectrum of application and their predictive capability in the evolution of physical systems.