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Sylvester is a big part of the folklore of mathematics, especially his interactions with Arthur Cayley. To help separate the truth from fiction, this book offers 140 of Sylvester's letters, selected from his extensive personal and professional correspondence over some 60 years. Parshall provides a context for each letter in addition to a detailed commentary on its historical and mathematical aspects. Specific to mathematics, the letters offer insight into Sylvester's life as a disadvantaged Jew in British academia, his creation of a research program in the now defunct theory of invariants, his key role in the development of graduate-level mathematics and a research community in American universities, and his contributions to the fields of group theory, matrix theory, and determinants. . . . Highly recommended for anyone interested in advanced mathematics or the history of mathematics, plus those interested in 19th-century developments specific to British and American society. --Choice<br> The volume under review is a long-overdue corrective to the legends that have grown up around Sylvester. Here he appears in his own words and those of his correspondents . . . in a selection comprising about 12% of the 1200 letters that have been preserved. . . . [E]ach of the letters included in the volume illustrates a significant episode in Sylvester's life or works. . . . From the mathematical point of view the letters to and from Cayley, Hermite, and others will be of most interest . . . For those with an interest in the history of invariant theory . . . there is a wealth of source material here. And, of course, there are all the famous clashes that Sylvester had with bureaucrats in bothAmerican and Britain over a variety of issues. . . . The book is very well edited and contains a generous bibliography and index. For those with an interest in Sylvester or the mathematics he created, it is well worth its price. --Mathematical Reviews<br> By comparison with his contemporaries, James Joseph Sylvester (1814-1897) . . . had an unconventional career. . . . Thirty-two of Sylvester's correspondents are brought together in this volume . . . In sum the letters make for intriguing reading and all the more so for Parshall's excellent editorial input. A short contextualising essay prefaces each chapter, and obscurities in the text--of which there are many, both literary and mathematical--are fully explained in detailed and well-informed footnotes which are complemented by an extensive bibliography. The book provides not just a portrait of Sylvester but it also digs deep into the heart of nineteenth-century Western mathematics teaching and research. Some of the mathematics discussed in the letters is challenging, particularly to twentieth-century eyes, but Parshall's commentary ensures that the thread is never lost, and the book is accessible to anyone with an interest in Sylvester or his period. --The Mathematical Association of America<br> This book is a selection of 140 letters...drawn from every part of (Sylvester's) career, and illuminate every aspect of his life. -- Archives Internationales D'Histoire Des Sciences, 1999, Vol 49<br>

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