The Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Professor S.-S. Chern. It was devoted to memorializing those two outstanding and original mathematicians who had made significant contributions to algebraic geometry and algebraic topology, respectively. It also provided a forum for leading mathematicians to expound and discuss their views on new ideas in these fields, as well as trends in 21st-century mathematics. About 100 mathematicians participated in the conference, including Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, and others. This volume contains selected papers presented at the conference. The topics include canonical maps of Gorenstein three-folds, fundamental groups of algebraic curves, Chen's interated integrals, algebraic fibre spaces, and more.