The field of mathematics that primarily deals with counting is known as combinatorics. It is used as a means and an end in obtaining results and in studying properties of finite structures. It addresses the problems of enumeration, construction, existence and optimization of these structures. The discipline has many sub-fields. Some of these are analytic combinatorics, extremal combinatorics, enumerative combinatorics, probabilistic and algebraic combinatorics. Coding theory, discrete and computational geometry, combinatorics and physics, combinatorics and dynamical systems, and combinatorial optimization are some of the fields that are closely related to this discipline. The field finds its application in logical and statistical physics, pure mathematics, geometry, topology, computer science and evolutionary biology. The book studies, analyzes and upholds the pillars of combinatorics and its utmost significance in modern times. It also unfolds the innovative aspects of this area of study which will be crucial for the holistic understanding of the subject matter. This book, with its detailed analyzes and data, will prove immensely beneficial to professionals and students involved in this area at various levels.