"It is the object of the present work to exhibit new algebras, in their detail, as being useful engines for the deduction of propositions; and in their several subordination to dominant ideas, as being representative symbolisms of fundamental conceptions. In conformity with this latter object I have not hesitated to compress, or even to omit, developments and applications, which are not allied to the dominant interpretation of any algebra. This unity of idea, rather than completeness is the ideal of this book" (Preface, p. viii). Whitehead's prelude to the three volume Principia Mathematica, which he wrote with Bertrand Russell in 1910-1913. Whitehead had planned a two-volume Universal Algebra just as Russell had planned a two-volume Principles of Mathematics (Volume I, 1903). Neither of them published a second volume to these works, abandoning them in favor of a collaboration on Principia. This volume is divided into seven books. In Book I, the general principles of the subject are discussed. Book II is devoted to the Algebra of Symbolic Logic. Book III deals with general principles of addition and the theory of the positional manifold. Book IV discusses principles of the Calculus of Extension. The final three books are devoted to the Calculus of Extension in relation to the theory of forces in a positional manifold of three dimensions, non-Euclidean geometry and the ordinary Euclidean space of three dimensions.