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This volume consists of a collection of papers devoted primarily to transcendental number theory and diophantine approximations written by the author. Most of the materials included in this volume are English translations of the author's Russian manuscripts, extensively rewritten and brought entirely up to date. These papers and other papers included in this volume were available to specialists in manuscript form, but this is the first time that they have been collected and published.Though the earlier papers have been preserved in the form in which they were prepared initially, the volume is organized in such a way as to reflect recent progress and to allow readers to follow recent developments in the field. As an introductory guide to the volume, the author included an expanded and updated text of his invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki. The appendix contains a paper on the extremality of certain multidimensional manifolds prepared by A. I. Vinogradov and the author in 1976. Chudnovsky received a MacArthur Foundation Fellowship in 1981.