General relativity came to life in 1915, when Albert Einstein formulated his field equations. These unify space, time, and gravitation, where the latter acts through curvature. Thereby the laws of physics obtain a geometric nature. Mathematical general relativity investigates spacetimes, which are manifolds equipped with a Lorentzian metric obeying the related Einstein-matter systems of nonlinear partial differential equations. The fruitful interactions of mathematics and physics in general relativity have produced breakthroughs in all the related research fields. This volume includes 14 articles presenting aspects of the most important general relativity research of the past 100 years. Among them we find cosmological and non-cosmological questions, the Cauchy problem for the Einstein equations, stability results, black holes and their formation, gravitational waves and their memory effect, the concept of energy, and the asymptotics of spacetimes. Through geometric analysis and advanced theory of nonlinear partial differential equations, long-standing problems have been solved lately that had remained locked since the beginnings of this beautiful theory of general relativity. Many more burning questions have been formulated and are yet to be answered.

During the 2015-2016 year, Harvard University's Center of Mathematical Sciences and Applications (CMSA) hosted a year-long thematic program on nonlinear equations and their connections to geometry, physics, and computer science. This volume presents articles contributed by some of the participants in this program, and builds on the activities of that special year. Specific topics include: general existence and regularity for elliptic and parabolic equations, the theory of minimal surfaces, the Weyl and Minkowski problems, transport and conservations laws, Navier-Stokes, and the Calderon problem. This volume, the second in the series, will benefit scholars working in nonlinear analysis and its connections with geometry and physics.

During the 2015-2016 year at Harvard University's Center of Mathematical Sciences and Applications (CMSA), several researchers working in mathematical general relativity presented lectures on modern topics of research in the field of "Non-linear Equations." This volume presents articles-by those researchers and their co-authors-drawn from their CMSA lectures. Specific topics include the Cauchy problem for the Einstein equations in cosmological and non-cosmological settings; investigation of stability as well as singularities (black holes) of classes of spacetimes; initial data engineering; gravitational radiation; and asymptotics of spacetimes, quasi-local energies, and their limits. The content of this volume reflects some of the activities at the Harvard CMSA during the 2015-2016 program, and provides insights into active areas of research in mathematical general relativity that can benefit scholars working in PDEs, geometric analysis, and general relativity.

The discovery of the expanding universe is one of the most exciting exploits in astronomy. This book explores its history, from the beginnings of modern cosmology with Einstein in 1917, through Lemaitre's discovery of the expanding universe in 1927 and his suggestion of a Big Bang origin, to Hubble's contribution of 1929 and the subsequent years when Hubble and Humason provided the essential observations for further developing modern cosmology, and finally to Einstein's conversion to the expanding universe in 1931. As a prelude the book traces the evolution of some of the notions of modern cosmology from the late Middle Ages up to the final acceptance of the concept of galaxies in 1925. Written in non-technical language, with a mathematical appendix, the book will appeal to scientists, students, and anyone interested in the history of astronomy and cosmology.