If [italic]K is a metrizable convex compact subset of a locally convex topological vector space, then all the following theorems hold for [italic]K: the Krein-Milman theorem on the extreme points of [italic]K; the Choquet integral representation theorem; the Bauer theorem on minimum points of concave lower semicontinuous functions on [italic]K. Roughly speaking, this memoir is devoted to extensions of these theorems to sets that are not compact and/or not convex.