Introduction; 1. The Laplacian on a Riemannian manifold; 2. Elements of differential geometry; 3. The construction of the heat kernel; 4. The heat equation approach to the Atiyah-Singer index theorem; 5. Zeta functions of Laplacians; Bibliography; Index.

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This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

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"The book is well written... This book provides a very readable introduction to heat kernal methods and it can be strongly recommended for graduate students of mathematics looking for a thorough introduction to the topic." Friedbert PrUfer, Mathematical Reviews

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