Index Theory is one of the most exciting and consequential accomplishments of twentieth-century mathematics. ""The Founders of Index Theory"" contemplates the four great mathematicians who developed index theory - Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I.M. Singer - through the eyes of their students, collaborators and colleagues, their friends and family members, and themselves. In addition to their own essays and correspondence - of historical importance - this volume presents a variety of material of a decidedly personal as well as compelling mathematical nature, written by some of their most notable students and long-time collaborators, including such leading current figures in mathematics and physics as Simon Donaldson, Edward Witten, and S.T. Yau. In these writings, one perceives the expansive influence of their work across various fields of mathematics and into theoretical physics. At a time when the long and illustrious careers of Atiyah, Hirzebruch, and Singer are being recognized with birthday celebrations at Edinburgh, in Europe, and in Massachusetts, this second edition of ""Founders of Index Theory"" remembers the late and much beloved Raoul Bott - in the affectionate words of those three men, as well as family members and long-time friends and colleagues. What emerges is the portrait of a compelling mathematical mind informed by a warm and magnetic personality that was both a joy and inspiration to those who knew him. This volume includes a generous collection of color and black-and-white photographs - many rarely seen - of the four principal figures together with their family, friends, and colleagues. These include numerous images of Bott dating from his early childhood to his last years at Harvard University. ""The Founders of Index Theory, Second Edition"" is a valuable portrayal of four men who transformed mathematics in a profound manner, and who belong to a class of researchers whose interest and influence transcend the conventional boundaries of mathematical fields.