Élie Joseph Cartan is one of the most important mathematical figures in the first half of the 20th century. Although recognition for his many accomplishments did not come until late in his career, his intellectual influence is still felt as modern mathematics develops. From the earliest point in his career, Cartan further developed Norwegian mathematician Marius Sophus Lie's group theory which concerned continuous groupsand symmetries within them. He interworked Lie's theory and the original means in which he studied its global properties with differential geometry, classical geometry, and topology. These combined areas are still a vital part of contemporary mathematics. Cartan also formulated many original theories based on his studies. Despite making such vital contributions to mathematics, Cartan was quite modest, good humored, and easy going. He was also a gifted and well-liked teacher who could break down his intricate theories for the consumption of an...