Singular Integral Operators Quantitative Flatness and Boundary Problems Introduction Geometric Measure Theory Calderon Zygmund Theory for Boundary Layers in UR Domains Boundedness and Invertibility of Layer Potential Operators Controlling the BMO Semi Norm of the Unit Normal Boundary Value Problems in Muckenhoupt Weighted Spaces Singular Integrals and Boundary Problems in Morrey and Block Spaces Singular Integrals and Boundary Problems in Weighted Banach Function Spaces. This monograph provides a state of the art self contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail with complete proofs emphasizing and elaborating on the link between the geometric measure theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students researchers and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis PDEs and geometric analysis – will find this text to be a valuable addition to the mathematical literature.