Algebra is the study of mathematical symbols and the rules of manipulating these symbols. It is essential in almost all of mathematics. Algebra encompasses solving elementary equations and the study of abstractions such as groups, rings, and fields. Elementary algebra comprises the basic parts of algebra whereas the more abstract aspects fall under abstract algebra or modern algebra. Elementary algebra is required for any study of mathematics, science, or engineering, as well as medicine and economics. Abstract algebra is used in advanced mathematics, and is studied primarily by professional mathematicians. This book is an essential guide for both academicians and those who wish to pursue this discipline further. The topics included herein on algebra are of utmost significance and bound to provide incredible insights to readers. This book aims to equip students and experts with the advanced topics and upcoming concepts in this area.