This textbook introduces physical geodesy. It treats the boundary-value theories of the discipline comprehensively, and provides insights to the theory of gravity reduction based on a spherical Earth model.

This book is for students who wish to thoroughly understand the material and to expand their knowledge and skills in mathematics for more advanced study and research in this discipline. The details of mathematical derivations included are a useful asset for instructors and researchers.

Jun-Yi Guo is a Professor of Teaching, Division of Geodetic Science, School of Earth Sciences, The Ohio State University. He holds a Bachelor of Engineering degree in geodesy from the Wuhan Technical University of Surveying and Mapping (now integrated into Wuhan University), China, and a Doctor of Science degree from the Catholic University of Louvain, Belgium. He is a theoretical/mathematical geodesist/geophysicist specializing in the modelling of physical systems and in physical-problem-specific methodologies of data analysis. His publications cover a wide range of topics including surface loading theory, formulation and detection of the inner core wobble, formulation of outer core flow, detection of the Slichter modes, processing of Level 1B and Level 2 data of the Gravity Recovery and Climate Experiment (GRACE) satellite mission, glacial isostatic adjustment (GIA), prediction of Earth orientation parameters (EOPs) etc. His long-term professional aspiration lies in advancingfundamental theories in geodesy and geophysics in global scale, particularly, the theory of Earth deformation, which is associated with variations of gravity and rotation of the Earth.

He was a professor of geodesy at the Wuhan University before joining The Ohio State University, and taught theoretical courses in both undergraduate and graduate levels. He wrote lecture notes of his own for the courses in "Physical Geodesy" and "Geophysics", leading to the publication of two textbooks (in Chinese). The present book is based on one of them, and is completely rewritten in regards to his improved understanding and the tremendous recent development of the discipline.

Chapter 1. Earth's Gravity Field and Some of its Properties.- Chapter 2. Elementary Potential Theory.- Chapter 3. Spherical Harmonics.- Chapter 4. Normal Gravity Field and Reference Earth Ellipsoid.- Chapter 5. Stokes' Theory and Beyond.- Chapter 6. Gravity Reduction.- Chapter 7. Molodensky's Theory and Beyond.- Chapter 8. Fundamentals of Computation and Determination.- Chapter 9. Flattening and Gravity Inside the Earth.