Mathematics is a fundamental science that is concerned with the study of quantity, structure, space and change through the use of abstraction and logic. These studies are approached from the disciplines of arithmetic, algebra, geometry and analysis. Logic, set theory, uncertainty, number theory, Riemann surfaces, etc. are significant sub-domains of mathematics. Applied mathematical domains of statistics, decision sciences and computational mathematics are of strategic importance in science, engineering, business and industry. This book strives to provide a fair idea about mathematics and to help develop a better understanding of the latest advances within this field. It covers in detail some existing theories and innovative concepts revolving around advanced mathematics and its applications. In this book, using case studies and examples, constant effort has been made to make the understanding of the difficult concepts of mathematics as easy and informative as possible for the readers.