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This summer graduate school will take place at the Harbin Institute of Technology, Harbin, China. The purpose of this summer school is to introduce some of the basic ideas and state-of–the-art methods of pure and applied mathematics to graduate students and reseachers. In particular there will be ten world's leading experts (3 Fields Medal, Wolf Prize, Crafoord Prize, Gauss Prize, COPSS President's Award, SIAM Kleinman Prize, SIAM Von Karman Prize, ICIAM Pioneer Prize, Former President of the International Mathematical Union, etc) to give a series of mini-courses.