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The A1Σu+-X1Σg+ UV spectrum of Mg2 has been investigated with high resolution employing Fourier-transform spectroscopy and laser excitation. Computer simulation and fit of line positions to the overlapping structures in the spectra yield precise transition frequencies. Starting with the well characterized ground state X1Σg+ from former work, we derived excited energy levels and report on the evaluation of the A1Σu+ excited state, which is found to interact with another electronic state, which we identify as the lower part of the (1)1Πu state. A coupled channels fit to the level energies of the upper state yields a reliable potential energy curve for the A1Σu+ state for the range of vibrational levels 1 ≤ v′ ≤ 46. A potential energy curve for the (1)1Πu state is proposed, but the (1)1Πu state is only characterized by its coupling to the A state, and no direct transition to a level of the (1)1Πu state could be uniquely identified due to the overlapping spectral structures