Recursive functions are representable as lambda terms, and de nability in the calculus may be regarded as a de nition of computability. This forms part of the standard foundations of computer science. Lambda calculus is the commonly accepted basis of functional programming languages � and it is folklore that the calculus is the prototypical functional language in puri ed form. The course investigates the syntax and semantics of lambda calculus both as a theory of functions from a foundational point of view, and as a minimal programming language. Synopsis Formal theory, xed point theorems, combinatory logic: combinatory completeness, translations between lambda calculus and combinatory logic � reduction: Church-Rosser theorem � Bohm's theorem and applications � basic recursion theory � lambda calculi considered as programming languages � simple type theory and pcf: correspondence between operational and denotational semantics � current developments. Relationship with other courses Basic knowledge of logic and computability in paper B1 is assumed.