These notes are essentially an expanded version of a few talks given at the Ecole Normale Superieure (Verdier Seminar) in the spring of 1980 by the under-signed as well as one talk by M.S Narasimhan. Some unpublished material figures in the notes : i) the moduli of vector bundles on singular (not necessarily irreducible) curves. Here one finds a complete generalisation of D'Souza's thesis [5] as well as a partial generalization of Oda-Seshadri [301 (it would be interesting to carry out a more detailed generalization of Oda-Seshadri). It would also be interesting to make a detailed study of the relation between this moduli space and the one on the normalization of the curve. Some work has been done by Gieseker in this connection (lectures of TIFR in 1979-80) ; in fact this work of Gieseker served as the catalyst for this investigation. ii) the non-existence of certain Poincare families. This proof is due to M. Nori. iii) the moduli space of vector bundles with level structures. This is related to the work of Drinfeld. We follow the definition of D. Mumford in an unpublished manuscript. D. Mumford defines this concept only for vector bundles (i.e only for torsion free sheaves). It would be interesting to investigate the connection between these varieties and those on singular curves.