|Died||23 February 1917 (aged 74)|
|Alma mater||Ecole Normale Supérieure (in Paris)|
|Awards||Sylvester Medal (1916)|
|Thesis||Sur les surfaces orthogonales (1866)|
|Doctoral advisor||Michel Chasles|
|Doctoral students||Émile Borel |
According to his birth certificate, he was born in Nîmes in France on 14 August 1842, at 1 am. However, probably due to the midnight birth, Darboux himself usually reported his own birthday as 13 August, e.g. in his filled form for Légion d'Honneur.
His parents were François Darboux, businessman of mercery, and Alix Gourdoux. The father died when Gaston was 7. His mother undertook the mercery business with great courage, and insisted that her children receive good education. Gaston had a younger brother, Louis, who taught mathematics at the Lycée Nîmes for almost his entire life. 
He studied at the Nîmes Lycée and the Montpellier Lycée before being accepted as the top qualifier at the École normale supérieure in 1861, and received his Ph.D. there in 1866. His thesis, written under the direction of Michel Chasles, was titled Sur les surfaces orthogonales. During his studies at the ENS, he also took lectures in Sorbonne University and Collège de France.
In 1870, he co-founded the journal Bulletin des sciences mathématiques et astronomiques, called "Darboux's Journal" by his contemporary mathematicians. The editorial board was also formed by the mathematicians Paul Émile Appell, Émile Borel, Jacques Hadamard and Amedeo Guillet, with Darboux in the role of President. The publishing house was the Henry Gauthier-Villars et Cle Éditeurs, located in Paris.
In 1872, Darboux married the Beauvaisian milliner Amélie Célina Carbonnier (1848-1911), daughter of Charles Louis Carbonnier, tailor, and Marie Victorine Anastase Hènocq. He and Célina had two children, Jean-Gaston (1870-1921), who was born at the time of the Siege of Paris and later became a marine zoologist at the Faculty of Science in Marseille, and Anaïs Berthe Lucie (1873-1970). 
He participated in the foundation of the École normale supérieure de jeunes filles in 1880, an institute that aimed at training female educators and ran parallel to the École normale supérieure on rue d'Ulm. Its first director was Julie Favre.
In 1884, Darboux was elected to the Académie des Sciences.
Darboux made several important contributions to geometry and mathematical analysis (see, for example, linear PDEs). He was a biographer of Henri Poincaré and he edited the Selected Works of Joseph Fourier.
In 1900, he was appointed the Academy's permanent secretary of its Mathematics section.
In 1902, he was elected to the Royal Society and the American Philosophical Society; in 1916, he received the Sylvester Medal from the Society. In 1908, he was a plenary speaker at the International Congress of Mathematicians in Rome. He continued to contribute to the French Bulletin des sciences mathématiques, even after 1916.
There are many things named after him:
1873. Sur une classe remarquable de courbes et de surfaces algébriques et sur la théorie des imaginaires. Gauthier-Villars.
Darboux's contribution to the differential geometry of surfaces appears in the four-volume collection of studies he published between 1887 and 1896; see links below for access to these texts.
1887–96. Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal. Gauthier-Villars:
1898. Leçons sur les systèmes orthogonaux et les coordonnées curvilignes. Tome I. Gauthier-Villars.
Media related to Gaston Darboux at Wikimedia Commons