After a thesis in mathematical logic, his early work was in field theory and valuation theory. He wrote on valuation rings and Witt vectors, and separability in infinite field extensions. He started writing on group extensions in 1942, and in 1943 began his research on what are now called Eilenberg–MacLane spaces K(G,n), having a single non-trivial homotopy group G in dimension n. This work opened the way to group cohomology in general. After introducing, via the Eilenberg–Steenrod axioms, the abstract approach to homology theory, he and Eilenberg originated category theory in 1945. He is especially known for his work on coherence theorems. A recurring feature of category theory, abstract algebra, and of some other mathematics as well, is the use of diagrams, consisting of arrows (morphisms) linking objects, such as products and coproducts. According to McLarty (2005), this diagrammatic approach to contemporary mathematics largely stems from Mac Lane (1948). Mac Lane also coined the term Yoneda lemma for a lemma which is an essential background to many central concepts of category theory and which was discovered by Nobuo Yoneda. Mac Lane had an exemplary devotion to writing approachable texts, starting with his very influential A Survey of Modern Algebra, coauthored in 1941 with Garrett Birkhoff. From then on, it was possible to teach elementary modern algebra to undergraduates using an English text. His Categories for the Working Mathematician remains the definitive introduction to category theory. Mac Lane supervised the Ph.Ds of, among many others, David Eisenbud, William Howard, Irving Kaplansky, Michael Morley, Anil Nerode, Robert Solovay, and John G. Thompson. In addition to reviewing a fair amount of his mathematical output, the obituary articles McLarty (2005, 2007) clarify Mac Lane's contributions to the philosophy of mathematics. Mac Lane (1986) is an approachable introduction to his views on this subject. Selected works 1997 (1941). A Survey of Modern Algebra (with Garrett Birkhoff). A K Peters. 1948, "Groups, categories and duality," Proceedings of the Nat. Acad. of Sciences of the USA 34: 263–67. 1995 (1963). Homology, Springer (Classics in Mathematics) (Originally, Band 114 of Die Grundlehren Der Mathematischen Wissenschaften in Einzeldarstellungen.) AMS review by David Buchsbaum. 1999 (1967). Algebra (with Garrett Birkhoff). Chelsea. 1998 (1972). Categories for the Working Mathematician, Springer (Graduate Texts in Mathematics) 1986. Mathematics, Form and Function. Springer-Verlag. 1992. Sheaves in Geometry and Logic: A First Introduction to Topos Theory (with Ieke Moerdijk). 1995. 2005. Saunders Mac Lane: A