Geometric Methods in Degree Theory for Equivariant Maps The book introduces conceptually simple geometric ideas based on the existence of fundamental domains for metric G spaces. A list of the problems discussed includes Borsuk Ulam type theorems for degrees of equivariant maps in finite and infinite dimensional cases extensions of equivariant maps and equivariant homotopy classification genus and G category elliptic boundary value problem equivalence of p group representations. The new results and geometric clarification of several known theorems presented here will make it interesting and useful for specialists in equivariant topology and its applications to non linear analysis and representation theory