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This paper gives an account of both the lambda-calculus and its close relative, the combinatory calculus, and explains why they are of such importance for computer software. The account includes the shortest and simplest proof of the Church-Rosser theorem, which appeared in a limited printing in August 1982. It includes a model of the combinatory calculus, also available in 1982 in a limited printing. In the last half-dozen years, some revolutionary new ideas for programming have appeared, involving the very fundamentals of the lambda-calculus and the combinatory calculus. A short introduction is given for a couple of these new ideas.