This study is a survey of the theory of the generalized-inverses of matrices as defined by Penrose. The material has been categorized under the following major areas: the Generalized-Inverse, the Reflexive Generalized-Inverse, the Least Squares Generalized-Inverse, the Left Weak Generalized-Inverse, the Right Weak Generalized-Inverse, and the Pseudo-Inverse of matrices.