The ISFMA-CIMPA School on"Differential Geometry:Theory andApplications"was held on 07 August-18 August 2006，in the building ofthe Chinese-French Institute for Applied Mathematics（ISFMA）,FudanUniversity,Shanghai,China.This school was jointly organized by theISFMA and the CIMPA（International Centre for Pure and AppliedMathematics）,Nice,France.About sixty participants from China,HongKong,France,Cambodia,India,Iran,Pakistan,Philippines,Romania,Russia,Sri-Lanka,Thailand,Turkey,Uzbekistan and Vietnam attendedthis highly successful event.
　　The first objective of this school was to lay down in a self-contained:and accessible manner the basic notions of differential geometry,suchasthe metric tensor,the Riemann curvature tensor,the fundamental formsof a surface,covariant derivatives,and the fundamental theorem of sur-face theory etc.Although this field is with good reasons often consideredas a"classical"one,it has been recently"rejuvenated",thanks to themanifold applications where it plays an essential role.
　　The second objective of this school was to present some of theseapplications,such as the theory of linearly and nonlinearly elastic shells,the implementation of numerical methods for shells,and mesh generationin finite element methods.
　　To fulfill these objectives,four series of lectures,each series compris-ing ten 50min-lectures,were delivered under the following titles:"In-troduction to differential geometry","Introduction to shell theory","Adifferential geometry approach to mesh generation",and"Numericalmethods for shells".This volume gathers the materials covered in theselectures.As such,this volume should be very useful to graduate studentsand researchers in pure and applied mathematics.
　　The organizers take pleasure in thanking the various organizations fortheir generous support:The ISFMA,the CIMPA,the French Embassyin Beijing,the Consulate General of France in Shanghai,the NationalNatural Science Foundation of China,Fudan University,Higher Educa-tion Press and World Scientific.Finally,our special thanks are due toMrs.Zhou Chun-Lian for her patient and effective work in editing thisbook.