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I know just the basics of sheaf theory and would like to ask about good references for "vector bundle over a projective spaces"?

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Because of the AG-tag I assume that you mean algebraic vector bundles, which are far less understood than the topological vector bundles. Perhaps you should make your question more precise: What do you like to know about vector bundles on projective spaces? Are you already familiar with the basic results such as Serre twists and the classification of line bundles? A general reference is:

Christian Okonek, Michael Schneider, Heinz Spindler, Vector bundles on complex projective spaces

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