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This book is composed of two texts, by R.L. Dobrushin and S.Kusuoka, each representing the content of a course oflectures given by the authors. They are pitched at graduatestudent level and are thus very accessible introductions totheir respective subjects for students and non specialists.CONTENTS: R.L. Dobrushin: On the Way to the MathematicalFoundations of Statistical Mechanics.- S. Kusuoka: DiffusionProcesses on Nested Fractals.