In 1952, Harry Markowitz published Portfolio Selection, a paper which revolutionized modern investment theory and practice. The paper proposed that, in selecting investments, the investor should consider both expected return and variability of return on the portfolio as a whole. The investor should select portfolios which are efficient in that they minimize portfolio variance for a given expected return. Markowitz`s full solution of the general mean-variance efficent set problem was formulated by him in 1956 and presented in the appendix to his 1959 book, Portfolio Selection. Though certain special cases of the general model have become widely known, both in academia and among managers of large institutional portfolios, the charactersistics of the general solution were not presented in finance books for students at any level. And although the results of the general solution are used in a few advanced portfolio optimization programs, the solution to the general problem should not be seen merely as a computing procedure. It is a body of propositions and formulas concerning the shapes and properties of mean-variance efficient sets with implications for financial theory and practice beyond those of widely known cases.