The fundamental results of A . Connes which determine a complete set of isomorphism classes for most injective factors are discussed in detail. After some introductory remarks which lay the foundation for the subsequent discussion, an historical survey of some of the principal lines of the investigation in the classification of factors is presented, culminating in the Connes-Takesaki structure theory of type I I I factors. After a discussion of injectivity for finite factors, the main result of the paper, the uniqueness of the injective I I 1 factor, is deduced, and the structure of I I ∞ and type I I I injective factors is then obtained as corollaries of the main result.