I use here the notation a + b for the logical sum of a and b, a b for the logical product of a and b, and a' for the negation of a. The capital letters stand for constants and the small letters for variables. The parameters A, B, C and D are called the discriminants of the operation. Similarly the most general function of one variable can be written in the form f(a) = A a + B a'. A relation between several elements of a Boolean algebra is expressed by one or more equations or inequations between such functions of the elements related. A common type of problem concerning the operations of these algebras is that of finding all operations which have a certain formal property. Another problem, and one which I here solve, is that of finding all the operations which have all formal properties in common with a given operation, and in particular to find all unique operations, that is, those that share all their formal properties with no one other operation. Wiener, in a paper to which I shall later refer, makes the statement It would seem that a system whose postulates deal with entities which occupy a unique position in it has in some sense received a more thoroughgoing analysis than one where this is not the case. I give here later a postulate system for Boolean algebras in terms of a fundamental operation which is unique in this sense, which, as we shall see is not true of systems based on the operations usually taken as fundamental, such as logical sum and product. Many postulate systems have been given for Boolean algebras. Of these, Huntington's first set of ten postulates,t has in a sense become the standard. Sheffer has given a set of only five postulates, using the one