This first volume of selected mathematical papers of Laurent Schwartz covers the first half of his work in Analysis and PDE. After a foreword by Claude Viterbo, followed by some pictures, the reader will find a notice about the scientific works, by Laurent Schwartz himself, a few documents (letters and preparatory lecture notes), Bernard Malgrange's presentation of the theory of distributions (the theory for which Laurent Schwartz received the Fields Medal in 1950), and selected papers from 1944 to 1954.