Topological tools in Nonlinear Analysis had a tremendous develop- ment during the last few decades. The three main streams of research in this field, Topological Degree, Singularity Theory and Variational Meth- ods, have lately become impetuous rivers of scientific investigation. The process is still going on and the achievements in this area are spectacular. A most promising and rapidly developing field of research is the study of the role that symmetries...