This volume is published in honor of the sixtieth birthdays of Professors Reiko Miyaoka and Keizo Yamaguchi, contributed by international researchers. On January 2011, the international conference 'Differential Geometry and Tanaka Theory — Differential System and Hypersurface Theory —' was held at the Research Institute for Mathematical Sciences (RIMS), Kyoto University in honor of their sixtieth birthdays. With deep admiration and respect, we dedicate the present volume to the two Professors. This volume contains one survey article and six research articles, recommended to researchers in related fields.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America