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This volume is published in honor of Professor Gu Chaohao, a renowned mathematician and member of the Chinese Academy of Sciences, on the occasion of his 70th birthday and his 50th year of educational work. The subjects covered by this collection are closely related to differential geometry, partial differential equations and mathematical physics ¿ the major areas in which Professor Gu has received notable achievements. Many distinguished mathematicians all over the world contributed their papers to this collection. This collection also consists of ¿Gu Chaohao and I¿ written by C N Yang, ¿The academic career and accomplishment of Professor Gu Chaohao¿ by T T Li and ¿List of publications of Professor Gu Chaohao¿.