Book reference for heat kernels on Riemannian geometry

Question

I am looking for an introduction to heat kernel on Riemannian manifolds and bundles over them. Also, I want to learn some basic about Spectral Geometry.

I found on the internet Heat Kernel and Analysis on Manifolds by Alexander Grigoryan, but unfortunately I don’t have access to this book. I’m also considering to read The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds by Steven Rosenberg.

Therefore, I appreciate any book or other sources (e.g. lecture note, survey).

My background knowledge is Introduction to Topological/Smooth/Riemannian Manifolds by John Lee.

Answer 1

You can access Heat Kernel and Analysis on Manifolds by Alexander Grigoryan. You can do so by purchasing it from the AMS website.

Anyways,

Here are some books that discuss the mentioned topics and i think you may find interest in:

(1): Heat Kernels and Dirac Operators

(2): Heat Kernels and Spectral Theory

(3): Lectures on spectral geometry

(4): Heat Kernel and Analysis on Manifolds

Hope i helped!

P.S: All of those are graduate/ research level textbooks/ notes.