Differential geodesy is concerned with the geometry of the gravity field of the Earth, which is of fundamental importance to both theoretical geodesy and geophysics. This monograph presents a unified treatment of the foundations of differential geodesy as proposed originally by Antonio Marussi and Martin Hotine in their work. The principal features of the Marussi-Hotine approach to theoretical aspects are given in the first five chapters (based on leg calculus), while the last five chapters are devoted to the fundamental ideas of the Marussi and Hotine theory. The text includes practical problems and is intended for use by research geodesists, graduate students in geodesy, and theoretical geophysicists.

Apart from Hotine's work on Mathematical Geodesy, several previously unpublished reports are collected in this monograph, complemented by extensive comments on these contributions and a complete bibliography of Hotine by the editor.

Just as in the era of great achievements by scientists such as Newton and Gauss, the mathematical theory of geodesy is continuing the tradition of producing exciting theoretical results, but today the advances are due to the great technological push in the era of satellites for earth observations and large computers for calculations. Every four years a symposium on methodological matters documents this ongoing development in many related underlying areas such as estimation theory, stochastic modelling, inverse problems, and satellite-positioning global-reference systems. This book presents developments in geodesy and related sciences, including applied mathematics, among which are many new results of high intellectual value to help readers stay on top of the latest happenings in the field.

These proceedings contain 23 papers, which are the peer-reviewed versions of presentations made at the Joint Scientific Assembly of the International Association of Geodesy (IAG) and the International Association of Seismology and Physics of the Earth’s Interior (IASPEI). The assembly was held from 30 July to 4 August 2017 in Kobe, Japan. The scientific assembly included seven symposia organized by IAG, and nine joint symposia, along with additional symposia organized by IASPEI. The IAG symposia were structured according to the four IAG Commissions and the three GGOS Focus Areas, and included reference frames, static and time-variable gravity field, Earth rotation and geodynamics, multi-signal positioning, geodetic remote sensing, and GGOS. The joint symposia included monitoring of the cryosphere, studies of earthquakes, earthquake source processes, and other types of fault slip, geohazard warning systems, deformation of the lithosphere, and seafloor geodesy. Together, the IAG and joint symposia spanned a broad range of work in geodesy and its applications.