2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159682This is the first part of a 2 part survey on the functor of the big and p-adic Witt vectors.This is the first part (of two parts) of a survey on the Witt vectors. A preprint version of a chapter for the Handbook of Algebra. There are 148 pages. Comments, criticims, suggestions, etc. welcomeRings and AlgebrasCombinatorics16W30text