Over the last forty years, interest has arisen in the study of modern algebraic systems like Rings, Modules over Rings. The concept “Dimension” of a vector space, when generalized to modules becomes the concept “Goldie Dimension”. This dimension concept was studied by several authors from different continents. Success of fuzzy logic in a wide range applications inspired much interest in fuzzy logic among mathematicians. The researchers in mathematics were trying to introduce and study the concept of fuzzyness in different mathematical systems under study. Dr Bhavanari Satyanarayana & his Research Group studied Goldie Dimension and Spanning Dimension in Modules and N-groups. Also introduced the concept Fuzzy Dimension in Modules over Associative Rings. This monograph covers a vital study of several important concepts like: Goldie Dimension, Fuzzy submodule, Fuzzy Dimension, Fuzzy Basis in Modules over Associative Rings. This monograph is certainly attracts the interest of all algebraists, Ring Theorists, in particular. This monograph is a more valuable addition not only to the Institutional Libraries, but also to each personal library of every algebraist of the world.