In the thesis we describe Seiberg-Witten theory, in particular we focus on its connection with the intersection form. In the first part we summarize some of the gauge theory. Next, spin geometry, Clifford algebras and spin representations are discussed. In chapter 4 we introduce spin connection and Dirac operator. The core of the thesis is chapter 5 and 6 where Seiberg-Witten moduli space, equations and invariants are elaborated with some properties. In chapter 7 we dive in 4-dimensional topology and intersection form as its invariant.
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