Bolzano's (1781-1848) interests mirrored those of the 19th century, including theology, philosophy, ethics, politics, logic and mathematics. His work was all of a piece, so to study one discipline requires studying his complete works. In an effort to make more of Bolzano's work available in English, this new translation offers a representative selection of the mathematical work. In geometry and foundations the titles include Considerations on Some Objects of Elementary Geometry and Contributions to a Better-Grounded Presentation of Mathematics. Early works of analysis include such topics as the binomial theorem and as a consequence from it the polynomial theorem, purely analytic proof of the theorem and three problems of rectification, complanation and cubature ("as a sample of a complete organization of the science of space"), with later analysis and the infinite represented by pure theory of numbers, theory of functions and improvements, and paradoxes of the infinite. The editors provide notes on translation issues and a list of selected works