Abstract: We describe moduli spaces of semi-stable vector bundles on non-Kaehler elliptic complex surfaces and on non-Kaehler principal elliptic bundles, which are Calabi-Yau type 3-folds.

The main technical tools used are twisted Fourier-Mukai transform and a spectral cover construction. (Joint works with R. Moraru, A. Halaney and G. Trautmann).