Mathematical logic is the study of formal languages and reasoning within mathematics. One of the main historical uses of logic has been providing rigorous foundations of mathematics, but it has also been extensively applied to other areas of mathematics and beyond.

The University of Manchester has a long and distinguished tradition in logic, dating back at least to the time of Alan Turing (1912-1954). Research in logic at Manchester is currently focused on model theory and categorical logic, and their connections to other parts of mathematics. Model theory studies mathematical structures using logical tools, and has seen several major applications to diverse areas of pure mathematics, including number theory, algebra, and geometry. Categorical logic studies logic using techniques of category theory, which has led to many surprising applications in algebra, topology, and computer science.