The present issue is dedicated to the memory of Yvonne Choquet-Bruhat, who recently passed away at 101 years old. She was the first woman elected at the French Academy of Sciences and a remarkable mathematician. She pioneered the field of mathematical general relativity with her seminal 1952 paper on the local solvability of the Einstein equations. Her subsequent influential works on the constraint equations and on the evolution problem have left a deep impact on both theoretical and numerical developments.

The first text in this special issue, by Piotr Chruściel, is written in her honor. The rest of the volume consists of a collection of reviews on various aspects of general relativity from a mathematical perspective, many of them originating from the work of Yvonne Choquet-Bruhat. The following topics are covered:

1. “A survey on the positive mass theorem for asymptotically flat initial data sets" by Lan-Hsuan Huang;
2. “Gluing for the Einstein constraint equations" by Justin Corvino;
3. “The stability of Minkowski space and its influence on the mathematical analysis of general relativity" by Jacques Smulevici;
4. “The black hole stability problem" by Sergiu Klainerman;
5. “On the regularity problems of the Einstein equations" by Qian Wang;
6. “Weak Cosmic Censorship, trapped surfaces, and naked singularities for the Einstein vacuum equations" by Yakov Shlapentokh-Rothman;
7. “The Strong Cosmic Censorship conjecture" by Maxime Van de Moortel;
8. “Cosmology, the Big Bang and the BKL conjecture" by Hans Ringström;
9. “Burnett’s conjecture in general relativity" by Arthur Touati;
10. “Some aspects of spectral and microlocal methods in general relativity" by Dietrich Häfner.

We hope that these surveys will allow the reader to gain insights into the latest developments of the field, as well as to appreciate the tremendous achievements that have been obtained along the way, starting with the pioneering contributions of Yvonne Choquet-Bruhat.

Jérémie Szeftel, February 2025.

Photographer: Jean-François Dars.