Fuzzy Algebra has witnessed a rapid growth in the last two or three decades. However, a very few books exists on the topic. The interested researchers have no option left than to rely upon the resources available in the journals only. A systematic representation of the contents in the form of a book would be a object of ready reference which can speed up the research activities in the research community. This book provides an insight to the fuzzification of some of the relatively newer concepts of fuzzy algebra such as Gamma-Semigroups, RGamma-Modules, Tensor-products etc. It further incorporates notions of localization and primary decomposition in commutative algebra into fuzzy environment. Text emphasizes connections between algebra and topology, in the last chapter. Examples are included wherever seen to be relevant. It is suitable for senior undergraduate students, graduate students,researchers who deal with subjects of fuzzy algebra and fuzzy algebraic topology. It requires the reader only to have a familiarity with the topics developed in Basic Commutative Algebra.