I've been researching instantons lately and I'd like to learn more about them but would like some help finding what to read. I have read about the ADHM equations and their noncommutative analogues. But this only works for $\mathbb{R}^4$ and $\mathbb{R}^4_{NC}$. How do we extend these to other manifolds? For example, how can we get instantons on the torus $\mathbb{T}^4 = \mathbb{R}^4 / \Gamma$? Or a complex torus $\mathbb{T}_{\mathbb{C}}^2$? One would think to allow some sort of periodicity which agrees with the lattice (forgive the non-technical terminology), but how is this done and/or what are the obstructions to this?

The ADHM construction is such a beautiful thing and I hope there are analogues for other manifolds.

In summary I am looking for papers/notes/books to read that give an expository and/or technical explanation about finding instantons on other manifolds, particularly on the (complex, ideally) torus, which hopefully have a hand in the ADHM pot as well. And I'm not a physicist nor an analyst so the more algebro-/complex-geometric the better. Thanks for the help.