This book provides a comprehensive introduction to harmonic function theory, a fundamental topic in mathematics, physics, and engineering. It is designed to make learning about harmonic functions easier, starting from the basics and assuming only a solid foundation in real and complex analysis, along with some knowledge of functional analysis. The text includes simplified proofs, new material not typically covered in standard treatments, and a variety of exercises. It also includes a software package for symbolic calculations related to harmonic function theory, which can significantly reduce the time required for complex computations. The book is structured into chapters covering various aspects of harmonic functions, including their basic properties, 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. Appendices provide additional information on volume, surface area, and integration on spheres, as well as an overview of harmonic function theory and Mathematica. The authors have made several major changes in the second edition, including a new and simplified treatment of spherical harmonics, a formula for the Laplacian of the Kelvin transform, and a proof that the Dirichlet problem for the half-space with continuous boundary data is solvable. The book also includes generalized versions of Liouville's and Bôcher's Theorems, showing their equivalence. The authors also thank their students and readers for their contributions, as well as mathematicians who have influenced their understanding of harmonic function theory. They also acknowledge the support of their publisher and the mathematics editors. The book aims to provide an enjoyable and enlightening experience for readers, encouraging them to discover mathematics through lively discussions and problem-solving.This book provides a comprehensive introduction to harmonic function theory, a fundamental topic in mathematics, physics, and engineering. It is designed to make learning about harmonic functions easier, starting from the basics and assuming only a solid foundation in real and complex analysis, along with some knowledge of functional analysis. The text includes simplified proofs, new material not typically covered in standard treatments, and a variety of exercises. It also includes a software package for symbolic calculations related to harmonic function theory, which can significantly reduce the time required for complex computations. The book is structured into chapters covering various aspects of harmonic functions, including their basic properties, 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. Appendices provide additional information on volume, surface area, and integration on spheres, as well as an overview of harmonic function theory and Mathematica. The authors have made several major changes in the second edition, including a new and simplified treatment of spherical harmonics, a formula for the Laplacian of the Kelvin transform, and a proof that the Dirichlet problem for the half-space with continuous boundary data is solvable. The book also includes generalized versions of Liouville's and Bôcher's Theorems, showing their equivalence. The authors also thank their students and readers for their contributions, as well as mathematicians who have influenced their understanding of harmonic function theory. They also acknowledge the support of their publisher and the mathematics editors. The book aims to provide an enjoyable and enlightening experience for readers, encouraging them to discover mathematics through lively discussions and problem-solving.