TL;DR
This paper provides an accessible introduction to gauge theory, focusing on the Seiberg--Witten invariants, and aims to serve as foundational lecture notes for understanding gauge-theoretic approaches to manifold invariants.
Contribution
It offers a clear, introductory presentation of gauge theory concepts and their application to manifold invariants, especially Seiberg--Witten theory, suitable for newcomers.
Findings
Explains the basics of gauge theory and manifold invariants.
Details the Seiberg--Witten gauge theory as a key example.
Prepares readers for further study in gauge-theoretic invariants.
Abstract
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.
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