Algebra is a fundamental area of mathematics that manipulates symbols for solving equations and studying various abstractions. Elementary algebra and abstract algebra are the two primary branches of algebra. Elementary algebra uses variables to denote quantities or general numbers. It is mostly concerned with the solution of linear equations, quadratic equations, exponential and logarithmic equations, radical equations and systems of linear equations. Abstract algebra is the study of algebraic structures such as fields, groups, rings and vector spaces. It is used in many fields of science and mathematics. This book is a compilation of chapters that discuss the most vital concepts in the field of algebra. It attempts to understand the multiple branches that fall under the discipline of algebra. In this book, constant effort has been made to make the understanding of the difficult concepts of algebra as easy and informative as possible, for the readers.