During the years 1903-1914， Ramanujan recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature， most were not. Almost a decade after Ramanujan's death in 1920， G. N. Watson and B. M. Wilson began to edit Ramanujan's notebooks， but they never completed the task. A photostat edition， with no editing， was published by the Tata Institute of Fundamental Research in Bombay in 1957.This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Part I， published in 1985， contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan's quarterly reports. Part II， published in 1989， comprises accounts of Chapters 10-15 in the second notebook. Part III， published in 1991， provides an account of Chapters 16-21 in the second notebook. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the tlurd notebook. We also shall prove those results in the first notebook that are not found in the second or third notebooks. For those results that are known， we provide references in the literature where proofs may be found. Otherwise， we give complete proofs.
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