Republication of: On the initial value problem of the equations of gravitation

This is an English translation of a paper by Karl Stellmacher, first published in German in 1938, in which he presented the first, correct and successful, formulation of the initial value problem for Einstein’s equations in vacuum and with a dust source. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Helmut Friedrich and Stellmacher’s brief biography written by Hubert Goenner.