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. This new edition is published in two volumes on the occasion of the 100th anniversary of Stieltjes' death (1894). Besides the reproduction of Stieltjes' papers, the new edition contains a short biography and about 75 pages of commentaries by important mathematicians who are discussing the impact of Stieltjes' work on the development of the theory of orthogonal polynomials and continued fractions. In particular, Stieltjes' claim to have proven the Riemann hypothesis is discussed. The work is especially of interest for those mathematicians working in the above fields, but also for others who are anxious to know about the impact of Stieltjes on modern mathematics. It is incredible to see the achievements of Stieltjes who died so early, at the age of 38. One meets an extraordinary genius, who worked at the frontiers of knowledge. He lived in Leiden and later he emigrated (mainly through his intesive contacts with C. Hermite) to Toulouse where he became "professeur de calcul differentiel et integral" at the Faculty of Sciences. An English translation of his main paper "Recherches sur les fractions continues" is included in the present new edition.