A hybrid system is a dynamical system exhibiting both continuous and discrete behaviors. Motivated by the multiplication of ''discrete'' embedded computing devices interacting with the ''continuous'' physical world, the research on hybrid systems has rapidly developed since the nineties at the intersection of computer science, control theory and applied mathematics. This thesis presents our theoretical and methodological contributions to this field. In a first part, we introduce an approximation framework that applies to dynamical systems that can be continuous, discrete or hybrid; applications, including some in the field of symbolic control, are presented. The second part deals with reachability analysis, a computational technique which is very useful for the analysis of hybrid systems. Finally, the third part presents our contributions to multi-agent dynamical systems.
