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The purpose of these notes is to give a self-contained introduction to Witt vectors. We cover both the classical p-typical Witt vectors of Teichmüller and Witt [4] and the generalized or big Witt vectors of Cartier [1]. In the approach taken here, all necessary congruences are isolated in the lemma of Dwork. A slightly different but very readable account may be found in Bergman [3, Appendix]. We conclude with a brief treatment of special λ-rings and Adams operations. We refer the reader to Langer-Zink [2, Appendix] for a careful analysis of the behavior of the ring of Witt vectors with respect to étale morphisms.

Let N be the set of positive integers, and let S⊂ N be a subset with the property that, if n∈ S, and if d is a divisor in n, then d∈ S. We then say that S is a truncation set. The big Witt ring WS (A) is defined to be the set AS equipped with a ring structure such that the ghost map