  I discuss in these lectures vortex-like classical solutions to the equations
of motion of gauge theories with spontaneous symmetry breaking. Starting from
the Nielsen-Olesen ansatz for the Abelian Higgs model, extensions to the case
in which gauge dynamics is governed by Yang-Mills and Chern-Simons actions are
presented. The case of semilocal vortices and also the coupling to axions is
analyzed. Finally, the connection between supersymmetry and the existence of
first order BPS equations in such models is described.
