  Recent theoretical studies of various strongly-correlated systems in
condensed matter physics reveal that the lattice gauge theory(LGT) developed in
high-energy physics is quite a useful tool to understand physics of these
systems. Knowledges of LGT are to become a necessary item even for condensed
matter physicists. In the first part of this paper, we present a concise review
of LGT for the reader who wants to understand its basics for the first time.
For illustration, we choose the abelian Higgs model, a typical and quite useful
LGT, which is the lattice verison of the Ginzburg-Landau model interacting with
a U(1) gauge field (vector potential). In the second part, we present an
account of the recent progress in the study of ferromagnetic superconductivity
(SC) as an example of application of LGT to topics in condensed matter physics,
. As the ferromagnetism (FM) and SC are competing orders with each other, large
fluctuations are expected to take place and therefore nonperturbative methods
are required for theoretical investigation. After we introduce a LGT describing
the FMSC, we study its phase diagram and topological excitations (vortices of
Cooper pairs) by Monte-Carlo simulations.
