This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobayashis career. This is followed by two expository course lectures (the second part) on recent topics in extremal Kähler metrics and value distribution theory, which will be helpful for graduate students in mathematics interested in new topics in complex geometry and complex analysis. Lastly, the third part of the volume collects authoritative research papers on differential geometry and complex analysis.

Professor Shoshichi Kobayashi was a recognized international leader in the areas of differential and complex geometry. He contributed crucial ideas that are still considered fundamental in these fields. The book will be of interest to researchers in the fields of differential geometry, complex geometry, and several complex variables geometry, as well as to graduate students in mathematics.

1.Preface.- 2.Academic Genealogy of Shoshichi Kobayashi.- 3.About Professor Shoshichi Kobayashi.- 4.Shoshichi Kobayashis Publications.- 5.Course Lectures.- 5.1Toshiki Mabuchi (Osaka University): The Existence Problem of Extremal Kähler Metrics on Polarized Algebraic Manifolds.- 5.2Katsuhiro Yamanoi (Tokyo Institute of Technology): Kobayashi Hyperbolicity and Higher Dimensional Nevanlinna Theory.- 6.Contributed Articles: Jean Pierre Bourguignon, Akito Futaki, Nigel Hitchin, Gary Jensen, Shinichiro Matsuo, Joel Merker, Reiko Miyaoka, Hiraku Nakajima, Junjiro Noguchi, Takeo Ohsawa, Makiko Sumi Tanaka, Yoshihiko Suyama, Hajime Tsuji, Paul Vojta, Shing-Tung Yau, Jae-Hyun Yang, Keizo Hasegawa, and possibly others.