Sullivan’s MIT notes (Homotopy folder). Excellent stuff on localizations, completions, profinite, p-local and rational homotopy types. p-adic homotopy theory. Relation to etale homotopy theory! Remark: The Sullivan conjecture is about the contractibility of the space of maps from the classifying space of a finite group to a finite-dimensional CW complex.
nLab page on p-local homotopy type