The editors dedicate this volume to the late S.–S. Chern, one of the great mathematicians of the twentieth century, and a leader in the field of differential geometry. Chern made seminal advances in areas such as web geometry, integral geometry, complex geometry, Riemannian geometry, and Finsler geometry. He is well-known for the Chern-Simons theory, the Chern-Weil theory, and Chern classes. His brilliant research and teaching have exerted a deep and lasting influence on mathematics.

Presented herein are survey papers by mathematicians from around the world, particularly from China, who review the present state of the areas in which Chern worked, and discuss the various directions which those fields will take in the future. This collection contains valuable information useful to graduate students and researchers.