Spectral and Scattering Theory for Second-Order Partial Differential Operators is ideal for researchers and postgraduate students seeking to apply the spectral theory of second-order differential operators in exterior domains to their own field, and addresses the growing need for spectral transforms to deal with deep problems of analysis of partial differential equations. In additions to presenting the classical results of spectral and scattering theory, it also outlines recent work in the field including the scattering of Schrödinger operators on a star graph, uniform resolvent estimates, smoothing properties and Strichartz estimates, and other applications. Key Features, First book to bring together this material in an easily accessible and comprehensible form, Among the first texts devoted to the study of exterior problems for differential operators in terms of their spectral and scattering theory by non-abstract PDE related tools, Offers early-career researchers a useful guide to the essential techniques and structural properties of such spectral representations, Contains results with wide applications to different types of PDEs Book jacket.