Algebra is a sub-division of mathematics that involves elementary equation solving and study of abstractions. Advanced algebra or abstract algebra is the study of algebraic structures such as groups, rings, fields, vector spaces, lattices, etc. Algebraic structures that involve single binary operations are magma, group, semigroup, monoid and quasigroup. Fields, modules, vector spaces, lie algebra, lattice, Boolean algebra, etc. are all examples of algebraic structures that involve several operations. This book is a compilation of chapters that discuss the most vital concepts and emerging trends in the field of advanced algebra. Such selected concepts that redefine this discipline have been presented in this book. It will serve as a valuable source of reference for graduate and post graduate students as well as experts.