The provided text is the preface and table of contents for the second edition of "Harmonic Function Theory" by Sheldon Axler, Paul Bourdon, and Wade Ramey. The book is part of the Graduate Texts in Mathematics series published by Springer Science+Business Media, LLC. It covers the fundamental properties and advanced topics in harmonic function theory, including bounded harmonic functions, positive harmonic functions, the Kelvin transform, harmonic polynomials, harmonic Hardy spaces, harmonic functions on half-spaces, harmonic Bergman spaces, the decomposition theorem, annular regions, and the Dirichlet problem. The authors aim to make the subject accessible to readers with a good foundation in real and complex analysis, while also presenting new and simplified proofs and additional material not typically covered in standard treatments. The second edition includes significant improvements such as a new treatment of spherical harmonics, a formula for the Laplacian of the Kelvin transform, and generalized versions of Liouville’s and Böcher’s Theorems. The authors have also developed a software package to assist with symbolic calculations in harmonic function theory. The book is based on a graduate course at Michigan State University, where the authors and their students engaged in lively discussions, leading to the development of this comprehensive and engaging text.The provided text is the preface and table of contents for the second edition of "Harmonic Function Theory" by Sheldon Axler, Paul Bourdon, and Wade Ramey. The book is part of the Graduate Texts in Mathematics series published by Springer Science+Business Media, LLC. It covers the fundamental properties and advanced topics in harmonic function theory, including bounded harmonic functions, positive harmonic functions, the Kelvin transform, harmonic polynomials, harmonic Hardy spaces, harmonic functions on half-spaces, harmonic Bergman spaces, the decomposition theorem, annular regions, and the Dirichlet problem. The authors aim to make the subject accessible to readers with a good foundation in real and complex analysis, while also presenting new and simplified proofs and additional material not typically covered in standard treatments. The second edition includes significant improvements such as a new treatment of spherical harmonics, a formula for the Laplacian of the Kelvin transform, and generalized versions of Liouville’s and Böcher’s Theorems. The authors have also developed a software package to assist with symbolic calculations in harmonic function theory. The book is based on a graduate course at Michigan State University, where the authors and their students engaged in lively discussions, leading to the development of this comprehensive and engaging text.