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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 of§lectures given by the authors. They are pitched at graduate§student level and are thus very accessible introductions to§their respective subjects for students and non specialists.§CONTENTS: R.L. Dobrushin: On the Way to the Mathematical§Foundations of Statistical Mechanics.- S. Kusuoka: Diffusion§Processes on Nested Fractals.