  In the mid 1990's Seiberg and Witten determined the exact low energy
effective action of $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge
group $SU(2)$. Later, in the early 2000's Nekrasov calculated this action
directly using localisation techniques. This work serves as an introduction to
the area, developing both approaches and reconciling their results.
