James Joseph Sylvester (1814–97) was an English mathematician who made key contributions to numerous areas of his field and was also of primary importance in the development of American mathematics, both as inaugural Professor of Mathematics at Johns Hopkins University and founder of the American Journal of Mathematics. Originally published in 1904, this book forms the first in four volumes of Sylvester's mathematical papers, covering the period from 1837 to 1853. Together these volumes provide a comprehensive resource that will be of value to anyone with an interest in Sylvester's theories and the history of mathematics.