The BPST-'t Hooft instanton solution is found and explained, as a solution of Euclidean Yang–Mills theory. After setting up the theory, we propose the self-duality equation and show that it minimizes the Euclidean action. On the self-dual condition, the action becomes the second Chern number, the integral of the Chern form and a topological number identified with the instanton number, and a configuration carrying it interpolates between different winding numbers for monopoles. The explicit instanton solution is found by an ansatz, and its action is calculated. We comment on the interpretation in the quantum theory, as governing transitions between different monopole number sectors.