In its originalformulation Lang's theorem referred to a semilinear map on an n-dimensional vectorspace over the algebraic closure of GF(p): it fixes the vectors of a copy ofV(n, p^h). In other words, every semilinear map defined over a finite field isequivalent by change of coordinates to a map induced by a field automorphism. We provide an elementaryproof of the theorem independent of the theory of algebraic groups and, as a by-product of ourinvestigation, obtain a convenient normal form for semilinear maps. We apply our theorem to classicalgroups and to projective geometry. In the latter application we uncover three simple yet surprisingresults.