This volume, "Elliptic Partial Differential Equations of Second Order" by David Gilbarg and Neil S. Trudinger, is a comprehensive treatise on the theory of second-order quasilinear elliptic partial differential equations, with a focus on the Dirichlet problem in bounded domains. It grew out of lecture notes from graduate courses at Stanford University and includes preparatory chapters on potential theory and functional analysis to make the content accessible to a broad audience. The book covers a wide range of topics, including linear equations, classical solutions, Sobolev spaces, generalized solutions, and quasilinear equations. It also delves into advanced topics such as maximum and comparison principles, topological fixed point theorems, and equations of mean curvature type. The authors acknowledge the contributions of numerous individuals and the support from the National Science Foundation. The book is part of the "Grundlehren der mathematischen Wissenschaften" series and is available in both hardcover and eBook formats.This volume, "Elliptic Partial Differential Equations of Second Order" by David Gilbarg and Neil S. Trudinger, is a comprehensive treatise on the theory of second-order quasilinear elliptic partial differential equations, with a focus on the Dirichlet problem in bounded domains. It grew out of lecture notes from graduate courses at Stanford University and includes preparatory chapters on potential theory and functional analysis to make the content accessible to a broad audience. The book covers a wide range of topics, including linear equations, classical solutions, Sobolev spaces, generalized solutions, and quasilinear equations. It also delves into advanced topics such as maximum and comparison principles, topological fixed point theorems, and equations of mean curvature type. The authors acknowledge the contributions of numerous individuals and the support from the National Science Foundation. The book is part of the "Grundlehren der mathematischen Wissenschaften" series and is available in both hardcover and eBook formats.