The Einstein Gravity Explorer mission (EGE) is devoted to a precise measurement of the properties of space-time using atomic clocks. It tests one of the most fundamental predictions of Einstein's Theory of General Relativity, the gravitational redshift, and thereby searches for hints of quantum effects in gravity, exploring one of the most important and challenging frontiers in fundamental physics. The primary mission goal is the measurement of the gravitational redshift with an accuracy up to a factor 104 higher than the best current result. The mission is based on a satellite carrying cold atom-based clocks. The payload includes a cesium microwave clock (PHARAO), an optical clock, a femtosecond frequency comb, as well as precise microwave time transfer systems between space and ground. The tick rates of the clocks are continuously compared with each other, and nearly continuously with clocks on earth, during the course of the 3-year mission. The highly elliptic orbit of the satellite is optimized for the scientific goals, providing a large variation in the gravitational potential between perigee and apogee. Besides the fundamental physics results, as secondary goals EGE will establish a global reference frame for the Earth's gravitational potential and will allow a new approach to mapping Earth's gravity field with very high spatial resolution. The mission was proposed as a class-M mission to ESA's Cosmic Vision Program 2015-2025. © Springer Science + Business Media B.V. 2008.