This is the first research-level monograph to be written on this vast and multi-faceted subject on the interface of mathematics and theoretical physics. The book gives a unified account of what is known established theory and a state-of-the-art account of what is still developing. The mathematical content is not easy but the results are nevertheless in demand not only from physicists but from engineers working for example in semi-conductors and composite materials and other branches of chemical engineering. The book contains many concrete examples for such applications.