Quantum Schubert Calculus

This paper works out the versions of the classical Giambelli and Pieri formulas in the context of quantum cohomology of a complex Grassmannian.Comment: 20 pages (LaTeX). To appear in Advances in Mathematics. The quantum Pieri formula in the original version has been corrected (see also alg-geom/9705024), and the Title has been ``quantized'