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We give a proof of the following theorem of M. Gromov (Oka's principle forholomorphic sections of elliptic bundles, J. Amer. Math. Soc., 2 (1989),851-897). Let Z be a holomorphic fiber bundle over a Stein manifold. If thefiber of Z admits a dominating holomorphic spray then the inclusion of thespace of global holomorphic sections of Z into the space of continuous sectionsis a weak homotopy equivalence. In the classical case when the fiber is acomplex Lie group or a homogeneous space this was proved by H. Grauert (Math.Ann., 135 (1958), 263--273). For further results in this direction see thepapers math.CV/0101040, math.CV/0101040, math.CV/0101034, math.CV/0101238,math.CV/0107039, math.CV/0110201.

Oka's principle for holomorphic fiber bundles with sprays