  This is lecture notes for a course given at the PCMI Summer School "Quantum
Field Theory and Manifold Invariants" (July 1 -- July 5, 2019). I describe
basics of gauge-theoretic approach to construction of invariants of manifolds.
The main example considered here is the Seiberg--Witten gauge theory. However,
I tried to present the material in a form, which is suitable for other
gauge-theoretic invariants too.
