This is a new annotated edition of Thomas J. Stieltjes' Collected Papers published earlier in 1914 (Vol. I) and 1918 (Vol. II) by Noordhoff, Groningen, in French. The new edition is published by Springer-Verlag in two volumes on the occasion of the 100th anniversary of Stieltjes' death (1894). This book is of great interest for all mathematicians anxious to understand the impact of Stieltjes' work on modern mathematics, and in particular on the theory of orthogonal polynomials and continued fractions. The book contains, besides the reproduction of Stieltjes' papers, about 75 pages of commentaries by contemporary mathematicians on Stieltjes' work as well as an English translation of his main paper "Recherches sur les fractions continues" and of his short note regarding the Riemann hypothesis.From the Preface by Gerrit van Dijk: "The present edition, which consists of two volumes, is mainly a reissue of the Oeuvres Complètes of Thomas Jan Stieltjes. I have added a short biography and four commentaries on parts of Stieltjes' work, written by specialists. Translations of his papers "Sur une fonction uniforme" and "Recherches sur les fractions continues" are also included. The first paper contains the "proof" of the Riemann hypothesis, and the second paper, which is generally considered to be his most important one, contains the introduction of the Stieltjes integral. A Bibliography of Stieltjes is included in both volumes for the convenience of the reader."