The principal contents of this book covers algebraic descriptions of nearly pseudocompact and nearly realcompact spaces. It has been shown in this book that equality of some special kinds of rings represents a space to be nearly pseudocompact. Furthermore a space to be Nearly realcompact characterizes a class of ideals (SRM ideal) to be fixed and finally it has been established that within the class of locally compact spaces, C(X) determines X when X is nearly realcompact. Further it was clearly described that the 'local compactness' condition can never be dropped. This book covers study of some special type of maps on nearly realcompact spaces and a detailed investigation of a new space, namely, hard pseudocompact space.Finally at the end of last chapter an example of a normal space is instantiated where the space with its hyper-real growth is not normal.