On the existence of three nonselfintersecting closed geodesics on manifolds homeomorphic to the 2-sphere

The author gives a complete proof of the Lyusternik–Shnirel'man theorem that on each smooth Riemannian manifold homeomorphic to the 2-sphere there exist at least three distinct nonselfintersecting closed geodesics (the proof by Lyusternik and Shnirel'man contains substantial gaps).