The Symposium'Gaia : at the frontiers of astrometry', held in Sèvres (Hauts de Seine, France) from 7 to 11 June 2010, was the closing conference of the European Marie Curie ELSA network (European Leadership in Space Astrometry). Gaia, selected as one of the cornerstones of the European Space Agency (ESA) Science Program in October 2000 and planned for launch in 2012, has been conceived in the wake of the success of the Hipparcos satellite, the first space astrometry mission, launched by ESA in 1989. Combining the power of discovery of a systematic and repeated survey of the sky with three complementary instruments (astrometric, photometric and spectroscopic) and extreme accuracy astrometry, Gaia will provide an unprecedented stereoscopic map of our Galaxy and the nearby universe. The objectives of the Symposium were to present the results obtained in the framework of the ELSA network on the various aspects of the preparation of the data analysis and scientific exploitation of the Gaia mission. The science expected from Gaia has been put in the 2015 context, and progresses on parallel or connected topics have been presented : progress on other astrometric satellites, performance of light detectors in astronomy, processing of massive data sets, especially in astronomy, real-time classification of transients, access to massive data sets, and propects for ground-based observations in complement to astrometry.