Over the past four decades, interest has been arisen in the study of modern algebraic systems like: Nearrings, Modules over Nearrings. The concept "Dimension" of a vector space, when generalized to modules becomes the concept "Goldie Dimension", introduced by Goldie. In this Monograph this concept was extended to N-groups and studied fundamental results. The Monograph also covers a vital study of several important concepts like Matrix Nearrings, IFP Ideal, Spanning Dimension, Direct systems. The concept of directed hypercube introduced and studied "graph of complement ideals of N-groups with FGD". The algebraic concept "Gamma Nearring" was introduced by Bhavanari Satyanarayana in 1984. This concept gamma nearring is a generalization of both the concepts Ring and Nearring. The Monograph also covers various Fuzzy aspects of Gamma Nearrings. This yields the interconnection between Nearrings, Graph and Fuzzy concepts. This Monograph is certainly attracts the interest of all Algebraists, Nearring 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.