Physical mathematics is a branch of theoretical mathematics that has been developed for finding solutions of complex physical problems of quantum gravity, string theory, super symmetry, etc. The subject builds on the advanced theoretical dimensions in physics and complex mathematical abstraction in algebra, group theory and topology. This book discusses the fundamentals as well as modern approaches of both physics and mathematics that are relevant to the growth of this discipline. It also unfolds the innovative dimensions of analysis in physical mathematics that are being explored. A number of latest researches have been included to keep the readers up-to-date with this emerging field of study.