These notes have been written for a Summer School, "Systèmes Dynamiques et Topologie en Petites Dimensions", which took place at the Institut Fourier, in June-July 1994. The goal was to provide simple proofs for the Jordan and Schoenflies theorems and to give a short introduction to the theory of locally connected continua and indecomposable continua, with applications in Dynamical Systems and the theory of attractors.