This book serves as an introduction to the topical question of classification of holomorphic vector bundles on complex projective spaces. It includes many examples, historical remarks, unsolved problems.

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Christian Okonek is Professor for mathematics at the University of Zurich. Michael Schneider was Professor for algebraic geometry at the University of Bayreuth, deceased in 1997. Heinz Spindler is Professor for mathematics at the University of Osnabr�ck.

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