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 (only available in one set) 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,...