This book develops in detail a comprehensive system of mathematical logic, which attains to a new level of generality through the treatment of indefinitely extended sequences of entities as single terms. In the structure of the system, sequences and classes figure as fundamental, the prepositional function being entirely eliminated. Propositions are construed as a kind of sequences; quantification and the various devices of the prepositional calculus are developed in terms of classes. Further contributions to theory and method are to be found throughout the treatment of classes and relations.