By Thibault Damour, Olivier Darrigol, Vincent Rivasseau

This e-book is the fourth in a sequence of lectures of the S´ eminaire Poincar´ e,whichis directed in the direction of a wide viewers of physicists and of mathematicians. The objective of this seminar is to supply updated information regarding common issues of serious curiosity in physics. either the theoretical and experimental elements are lined, with a few ancient history. encouraged by means of the Bourbaki seminar in arithmetic in its association, as a result nicknamed “Bourbaphi”, the Poincar´ e Seminar is held two times a yr on the Institut Henri Poincar´ e in Paris, with cont- butions ready prematurely. specific care is dedicated to the pedagogical nature of the shows so that it will ful?ll the aim of being readable by way of a wide viewers of scientists. This quantity includes the 7th such Seminar, held in 2005. it's dedicated to Einstein’s 1905 papers and their legacy. After a presentation of Einstein’s ep- temological method of physics, and the genesis of exact relativity, a cen- nary point of view is o?ered. The geometry of relativistic spacetime is defined intimately. unmarried photon experiments are provided, as a excellent cognizance of Einstein’s gentle quanta speculation. A formerly unpublished lecture by way of Einstein, which provides an illuminating standpoint on statistical physics in 1910, on the sunrise of quantum mechanics, is reproduced. the quantity ends with an essay at the ancient, actual and mathematical points of Brownian movement. We hopethatthe publicationofthis serieswill servethe group ofphy- cists and mathematicians on the graduate pupil or specialist point.