The theory of Lie superalgebras (or, as they are also called, Z? - graded Lie algebras) has undergone a remarkable evolution during the last few
years. At present the most important result in the theory seems to be the classification by V.G. Kac of the finite-dimensional simple Lie superalgebras over an algebraically closed field of characteristic zero.Our main objective is to give a self-contained and detailed presentation of this classification. Thus we shall not presuppose any knowledge of the theory of Lie superalgebras, however, we assume that the reader is familiar with the standard theory of Lie algebras.