Fundamental aspects of topological solitons in four dimensional gauge theories of physical interest will be introduced. The have vast number of applications in diverse fields of physics. Examples are the Dirac and 't Hooft-Polyakov monopoles, instantons in Yang-Mills theories, and vortices in Abelian Higgs model and in nonAbelian gauge theories. Basic notion of homotopy groups and algebraic geometry will be given. After a brief introduction to supersymmetry, the Seiberg-Witten solutions of N=2 supersymmetric gauge theories will be discussed, with some emphasis on the most recent theoretical developments in the related field.