The field of study which focuses on numbers, formulas and associated structures, shapes and the spaces which contained them, and quantities and their changes is known as mathematics. Advanced mathematics is involved in the study of problems which cannot be solved using basic mathematical methods. They require a detailed understanding of the fundamentals of mathematics and advanced mathematical models. The advanced mathematical methods are involved in the study of several topics in linear algebra and multivariate calculus. Some applications of these models are in areas such as statistics, operations research, computer science, econometrics, and mathematical economics. This book outlines the mathematical methods, systems and applications used in advanced mathematics in detail. It consists of the contributions made by scientists and leading experts in advanced mathematics. The book is an essential guide for both academicians and those who wish to pursue this discipline further.