A Thesis Submitted in partial fulfillment of the requirements for the Degree of Science by Malihe Bahalu Latin : Following Bass, a ring R has stable range 1 if ra + b = 1 in R implies that a + tb is a unit for some t \\in R, equivalently ar + b = 1 imples a + tb is a unit for some t \\in R. we extend this equivalence to an arbitrary module, and use it to define what we mean by a stable module. The proof that the stable range condition is right–left symmetric is due to Vaserstein. We begin with a far-reaching generalization of Vaserstein’s lemma to an arbitrary Morita context. This engenders the notion of a stable Morita context. These contexts are studied and extend many properties of rings with stable range1. Then all this is applied to the “standard context” of a module to define and investigate stable modules. These are a natural generalization of the stable range condition for a ring.