This book is a collection of selected papers on recent trends in the study of infinite discretegroups. The authors who contributed to this volume were invited plenary speakers at the International Conference on Group Theory:“Geometric, Com-binatorial and Dynamical Aspects of Infinite Groups” which was held in Gaeta, Italy, in June 1-6, 2003. The exceptional quality of their lectures and the great interest they arose among the almost two hundred conference participants from over twenty countries gave us, the organisers of the conference,the idea of this book. We are most grateful to the authors who have all responded with wonderful enthusiasm to our request for a contribution