This is the third volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience. These ideas faithfully relied the spirit of this multi-volume and the editors hope that it will become very useful for research, learning and teaching. We express our deepest gratitude to all contributors to this volume for their clearly written and elegant articles.