Seiberg-Witten theory was invented in 1994 shortly after the discovery of Donaldson invariants. The Seiberg-Witten theory admits a U(1) symmetry, which makes them far more computable than the SU(2)-symmetric Donaldson theory. In this talk, we will briefly introduce the background of spin geometry and Dirac operators, before diving into the Seiberg-Witten moduli and defining the Seiberg-Witten invariants. We start and conclude with a proof of the Thom conjecture using Seiberg-Witten theory. This application shows the power of Seiberg-Witten theory in studying the geometry and topology of 4-manifolds.