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Algebra is an area of mathematics that studies mathematical symbols and their rules of manipulation. It is instrumental in equation solving and in the study of abstractions like rings, groups and fields. Algebraic structures can be modified using the operations of addition, multiplication, subtraction, etc. and characterized by associativity, commutativity and finite dimension, among others. Some common algebraic structures are groups, lattices, vector spaces, modules, etc. Hybrid structures are also under the scope of algebra such as lie group, topological group, Archimedean group, ordered groups, rings and fields, etc. The areas of study in algebra can be divided into linear and multilinear algebra, associative and nonassociative rings and algebras, general algebraic systems, group theory, field theory and polynomials, besides many others. This book presents the complex subject of algebra in the most comprehensible and easy to understand language. It covers in detail some existing theories and innovative concepts revolving around algebra. This book is a complete source of knowledge on the present status of this important field.