In this thesis, we present an expanded account of A Crash Course on Stable Range , Cancellation, Substitution, and Exchange based on an article by T. Y. Lam (2004). The themes’ of cancellation, internal cancellation, substation and exchange have led to a lot of interesting research in the theory of modules over commutative and noncommutative rings. This thesis Written on the article of [A Crash Course on Stable range Cancellation, Substitution, and Exchange] by T.Y Lam (2004). At the first has shown that for a ring R left stable range of R and right stable range of R are equal and used notion sr(R) for stable range R. There are several variations on the notion of cancellation. For instance, for a given module A, if A = K ? N = K ?N’ with N ? N’, does it follow that K ? K? Cancellation problem led to introduction notions of internally cancellable and substitution. We highlight the notion of an internally cancellable module by showing that a von Neumann regular ring R (as a module over itself) satisfies internal cancellation iff R is unit-regular, and this is also shown to be equivalent to R having stable range 1. Another variation is the following: if B and C are direct summands of a module M with complementary summands isomorphic to a given module A, then B, C necessarily has a common direct complement in M? If the answer is always “yes”, the given module A is said to have the substitution property. In 1964, in studying the refinements of direct decompositions of algebraic systems, Crawley and Jonson introduced the notion of “exchange” and “finite exchange” in their ltr"