This publication includes all the mathematical papers of H.J.S. Smith in chronological order, enabling readers to trace the course of his mathematical studies and tastes. Most of the papers are in English, some of the papers or notes are in French. His work falls into three distinct groups: Geometry, Theory of Numbers, and Elliptic Functions. The first paper in Volume II [Mémoire sur quelques problèmes cubiques et biquadratiques] was a prize memoir for which, cojointly with another memoir, the Steinder Prize of the Berlin Academy was awarded. This publication also includes a Biographical Sketch by Charles H. Pearson; Recollections of Henry J.S. Smith by Jowett, Lord Bowen, J.L. Strachan-Davidson and Alfred Robinson; Introduction to the Mathematical Papers by the Editor, J.W.L. Glaisher.