  In these lecture notes, an introduction to topological concepts and methods
in studies of gauge field theories is presented. The three paradigms of
topological objects, the Nielsen-Olesen vortex of the abelian Higgs model, the
't Hooft-Polyakov monopole of the non-abelian Higgs model and the instanton of
Yang-Mills theory, are discussed. The common formal elements in their
construction are emphasized and their different dynamical roles are exposed.
The discussion of applications of topological methods to Quantum Chromodynamics
focuses on confinement. An account is given of various attempts to relate this
phenomenon to topological properties of Yang-Mills theory. The lecture notes
also include an introduction to the underlying concept of homotopy with
applications from various areas of physics.
