This book examines Aristotelian logic from historical, philological and systematic perspectives. It analyses Aristotelian sources and calculus in the Aristotelian tradition and develops an all-embracing calculus through dialectic synthesis. The initial aim is to gather the essential material from Aristotle’s different levels of logic and to convey them in a new way using a taut, precise and modern algebraic presentation. Because Aristotle was the undisputed authority in logic for over two thousand years and continued to exercise a strong influence until the end of the 19th century, his logic is not considered as a past historical phenomenon but as a ground-breaking, historically effective idea which continues to drive contemporary developments. For the same reason the author examines logicians who sought and achieved an optimisation of Aristotle’s logic, primarily Leibniz, Boole and Peano.