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Abstract: Given a complex reductive group G, there is expected to be a generalization of Donaldson-Thomas theory whose goal is to count, in an appropriate sense, stable principal G-bundles over a Calabi-Yau threefold. The standard Donaldson-Thomas theory arises when G is a general linear group. I will present some recent results on such a generalization when G is a classical group using the framework of quiver representations. The key new tool is a representation of Kontsevich and Soibelman's cohomological Hall algebra which is constructed from the cohomology of moduli stacks of quiver theoretic analogues of G-bundles.