Gilkey (mathematics, U. of Oregon) compiles into a single reference the many results that have been found recently in asymptotic formulas in the theory of Dirac and Laplace type operators. He focuses on the functorial and special case methods of computing asymptotic heat trace and heat content coefficients in the heat equation, and introduces results from the Seeley calculus and other methods. The formulas he presents can be applied in such areas as index theory, compactness theorems for moduli spaces of isospectral metrics, and zeta function regularization