It was in September 1906 that the predecessor of the IAG, the 'Internationale Erdmessung', th organized the 15 General Assembly at the Hungarian Academy of Sciences in Budapest. It was 95 years later, in September 2001, that the IAG returned to this beautiful city to hold its Scientific Assembly, IAG 2001, in the historical premises of the Academy. The meeting took place from September 2-7, 2001 and continued the tradition of Scientific Assemblies, started in Tokyo (1982) and continued in Edinburgh (1989), Beijing (1993) and Rio de Janeiro (1997). Held every four years at the midpoint between General Assemblies of the IAG, they focus on giving an integrated view of geodesy to a broad spectrum of researchers and practitioners in geodesy and geophysics. The convenient location of the main building of the Hungarian Academy in downtown Budapest and the superb efforts of the Local Organizing Committee contributed in a major way to the excellent atmosphere of the meeting. As at previous meetings, the scientific part of the program was organized as a series of symposia which, as a whole, gave a broad overview of actual geodetic research activities. To emphasize an integrated view of geodesy, the symposia did not follow the pattern of the IAG Sections, but focussed on current research topics to which several IAG Sections could contribute. Each symposium had 5 sessions with presented papers and poster sessions on two consecutive days.

This open access book contains 30 peer-reviewed papers based on presentations at the 27th General Assembly of the International Union of Geodesy and Geophysics (IUGG). The meeting was held from July 8 to 18, 2019 in Montreal, Canada, with the theme being the celebration of the centennial of the establishment of the IUGG. The centennial was also a good opportunity to look forward to the next century, as reflected in the title of this volume. The papers in this volume represent a cross-section of present activity in geodesy, and highlight the future directions in the field as we begin the second century of the IUGG. During the meeting, the International Association of Geodesy (IAG) organized one Union Symposium, 6 IAG Symposia, 7 Joint Symposia with other associations, and 20 business meetings. In addition, IAG co-sponsored 8 Union Symposia and 15 Joint Symposia. In total, 3952 participants registered, 437 of them with IAG priority. In total, there were 234 symposia and 18 Workshops with 4580 presentations, of which 469 were in IAG-associated symposia.

Geodesy as the science which determines the figure of the earth, its orientation in space and its gravity field as well as its temporal changes, produces key elements in describing the kinematics and the dynamics of the deformable body "earth". It contributes in particular to geodynamics and opens the door to decode the complex interactions between components of "the system earth". In the breathtaking development recently a whole arsenal of new terrestrial, airborne as well as satelliteborne measurement techniques for earth sciences have been made available and have broadened the spectrum of measurable earth parameters with an unforeseen accuracy and precision, in particular to resolve the factor time. The book focusses on these topics and gives a state of the art of modern geodesy.

This open access volume contains selected papers of the 2021 Scientific Assembly of the International Association of Geodesy – IAG2021. The Assembly was hosted by the Chinese Society for Geodesy, Photogrammetry and Cartography (CSGPC) in Beijing, China from June 28 to July 2, 2021. It was a hybrid conference with in-person and online attendants. In total, the Assembly was attended by 146 in-person participants and 1,123 online participants. The theme of the Assembly was Geodesy for a Sustainable Earth. 613 contributions (255 oral presentations and 358 poster presentations) covered all topics of the broad spectrum considered by the IAG: geodetic reference frames, Earth gravity field modelling, Earth rotation and geodynamics, positioning and applications, the Global Geodetic Observing System (GGOS), geodesy for climate research, marine geodesy, and novel sensors and quantum technology for geodesy. All published papers were peer-reviewed, and we warmly recognize the contributions and support of the Associate Editors and Reviewers.

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.

Advances in space-borne technologies lead to improvements in observations and have a notable impact on geodesy and its applications. As a consequence of these improvements in data accuracies, spatial and temporal resolutions, as well as the developments in the methodologies, more detailed analyses of the Earth and a deeper understanding of its state and dynamic processes are possible today. From this perspective, this book is a collection of the selected reviews and case-study articles that report the advances in methodology and applications in geodesy. The chapters in the book are mainly dedicated to the Earth’s gravity field theory and applications, sea level monitoring and analysis, navigation satellite systems data and applications, and monitoring networks for tectonic deformations. This collection is a current state analysis of the geodetic research in theory and applications in today’s modern world.

The text develops the principal aspects of applied Fourier analysis and methodology with the main goal to inculcate a different way of perceiving global and regional geodetic and geophysical data, namely from the perspective of the frequency, or spectral, domain rather than the spatial domain. The word "methods" in the title is meant to convey that the transformation of a geophysical signal into the spectral domain can be applied for purposes of analysis as well as rapid computation. The text is written for graduate students; however, Chapters 1 through 4 and parts of 5 can also benefit undergraduates who have a solid and fluent knowledge of integral and differential calculus, have some statistical background, and are not uncomfortable with complex numbers. Concepts are developed by starting from the one-dimensional domain and working up to the spherical domain, which is part of every chapter. Many concepts are illustrated graphically with actual geophysical data primarily from signals of gravity, magnetism, and topography.

These proceedings represent the worldwide picture of the state of the art of geodesy. The volume comprehensively covers the most recent results and supplies a good review of the new ideas developing in the field, opening a window to the future of geodesy.

The Global Geodetic Observing System (GGOS) has been established by the Int- national Association of Geodesy (IAG) in order to integrate the three fundamental areas of geodesy, so as to monitor geodetic parameters and their temporal varia- ?9 tions, in a global reference frame with a target relative accuracy of 10 or b- ter. These areas, often called ‘pillars’, deal with the determination and evolution of (a) the Earth’s geometry (topography, bathymetry, ice surface, sea level), (b) the Earth’s rotation and orientation (polar motion, rotation rate, nutation, etc. ), and (c) the Earth’s gravity eld (gravity, geoid). Therefore, Earth Observation on a global scale is at the heart of GGOS’s activities, which contributes to Global Change - search through the monitoring, as well as the modeling, of dynamic Earth processes such as, for example, mass and angular momentum exchanges, mass transport and ocean circulation, and changes in sea, land and ice surfaces. To achieve such an - bitious goal, GGOS relies on an integrated network of current and future terrestrial, airborne and satellite systems and technologies. These include: various positioning, navigation, remote sensing and dedicated gravity and altimetry satellite missions; global ground networks of VLBI, SLR, DORIS, GNSS and absolute and relative gravity stations; and airborne gravity, mapping and remote sensing systems.