But Einstein was not satisfied with the study of the special problem of Relativity for uniform motion, but tried, in a series of papers beginning from 1911, to extend it to the case of non-uniform motion. The last paper in the present collection is a translation of a comprehensive article which he contributed to the Annalen der Physik in 1916 on this subject, and gives, in his own words, the Principles of Generalized Relativity. The triumphs of this theory are now matters of public knowledge. Einstein is now only 45, and it is to be hoped that science will continue to be enriched, for a long time to come, with further achievements of his genius. Principle of Relativity INTRODUCTION. At the present time, different opinions are being held about the fundamental equations of Electro-dynamics for moving bodies. The Hertzian[9] forms must be given up, for it has appeared that they are contrary to many experimental results. In 1895 H. A. Lorentz[10] published his theory of optical and electrical phenomena in moving bodies; this theory was based upon the atomistic conception (vorstellung) of electricity, and on account of its great success appears to have justified the bold hypotheses, by which it has been ushered into existence. In his theory, Lorentz proceeds from certain equations, which must hold at every point of “Äther”; then by forming the average values over “Physically infinitely small” regions, which however contain large numbers of electrons, the equations for electro-magnetic processes in moving bodies can be successfully built up. In particular, Lorentz’s theory gives a good account of the non-existence of relative motion of the earth and the luminiferous “Äther”; it shows that this fact is intimately connected with the covariance of the original equation, when certain simultaneous transformations of the space and time co-ordinates are effected; these transformations have therefore obtained from H. Poincare[11] the name of Lorentz-transformations. The covariance of these fundamental equations, when subjected to the Lorentz-transformation is a purely mathematical fact _i.e._ not based on any physical considerations; I will call this the Theorem of Relativity; this theorem rests essentially on the form of the differential equations for the propagation of waves with the velocity of light.