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We give an introduction to normalization by evaluation and type-directed partial evaluation. We first present normalization by evaluation for a combinatory version of G枚del System T. Then we show normalization by evaluation for typed lambda calculus with 脽 and 驴 conversion. Finally, we introduce the notion of binding time, and explain the method of type-directed partial evaluation for a small PCF-style functional programming language. We give algorithms for both call-byname and call-by-value versions of this language.