 Bolzano’s presentation of logic in the modern sense is embedded in the vast Theory of Science (henceforth TS; a shorter introduction to Bolzano’s logic may be found in Bolzano 2004a). The best known innovations of this work belong to his variation logic: definitions of universal validity and analyticity, along with the creation of a complete system of extensional relations between propositions, the most important being compatibility, deducibility (consequence), and equivalence. Bolzano discovered the link between deducibility and conditional probability, according to which deducibility and incompatibility appear as two limit cases of conditional probability. He is also recognized for adopting an anti-psychologistic approach to logic, and for his contributions to semantics. Bolzano’s theory of the grounding relation (Abfolge) leading to a hierarchical order among the propositions of a deductive science is the first modern study of axiomatic systems. Moreover, the thorough discussions of concepts of logic and many other insights contribute to make the TS one of the classical works in logic and epistemology, on a par with those of Aristotle, Leibniz, and Frege. The extensive historical notes contained in it are a unique source for the history of logic. Although written in natural language, Bolzano’s logic represents a decisive breakthrough in the development of modern logic.