The Yang–Mills Equation
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We present the geometric model of pure gauge theory, including the basics concerning the structure of the classical configuration space, and derive the Yang-Mills equation from the classical action functional. Next, we study the theory of instantons in a systematic way: we present the BPST-instanton family and the famous ADHM-construction, including a partial proof that this construction yields all instanton solutions. Moreover, we study the instanton moduli space. Finally, we present the classical stability analysis of the Yang-Mills equation as developed by Bourguignon and Lawson and discuss non-minimal solutions.