  This text gives a rough, but linear summary covering some key definitions,
notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the
classical monograph by Barendregt. First, we define a theory of untyped
extensional lambda calculus. Then, some syntactic sugar, a system of
combinatory logic, and the fixed point theorem are described. The final section
introduces a topology on the set of lambda terms which is meant to explain an
illusory contradiction. Namely, functions defined on the set of lambda terms
are in the set of lambda terms itself, the latter being a countable set.
However, the functions on the set of lambda terms appear to be continuous with
respect to a topology of trees.
