Abstract: After a concise review of basic aspects of Donaldson-Witten theory, we will provide a systematic path integral derivation of K-theoretic Donaldson invariants for closed, smooth four-manifolds X. These invariants arise as correlation functions in 5d N=1 SU(2) super Yang-Mills theory on X×S^1, equipped with a partial topological twist along X. At particular values of the circle circumference, the system is governed by the 5d superconformal E1 theory, and the resulting topological invariants generalize the familiar Seiberg–Witten invariants. This is based on my work with H. Kim, J. Manschot, G.W. Moore, and R. Tao, arXiv: 2509.23042.