Editorial note to: Georges Lemaître, A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae

This is an editorial note to accompany printing as a Golden Oldie in the Journal of General Relativity and Gravitation of the fundamental article by Georges Lema\^itre first published in French in 1927, in which the author provided the first explanation of the observations on the recession velocities of galaxies as a natural consequence of dynamical cosmological solutions of Einstein's field equations, and discovered the so-called Hubble law. We analyze in detail the scientific contents of this outstanding work, we describe how it remained unread or poorly appreciated until 1930, and we list and explain the differences between the 1927 and 1931 versions. Indeed the English translation published in 1931 in MNRAS was not perfectly faithful to the original text - it was updated. As it turned out very recently, the updates were done by Lema\^itre himself, but the discrepancies between the two texts caused a temporary stir among historians. Our new translation - given in the Appendix - follows the 1927 version exactly.