A detailed account of the Lense-Thirring effect and its implications for physics and astrophysics. Starting from a profound intuition of Lense and Thirring in 1918, based on a simple solution to the linearized Einstein field equations, this has emerged in the past four decades as a phenomenon of extraordinary importance in cosmology, radio jets in quasars, and the physics of neutron stars and black holes, besides leading to some of the most sophisticated experiments ever performed in the space surrounding our planet. The volume contains the contributions presented at the "Third William Fairbank Meeting", which have been expanded by adding a complete set of classical and prominent contemporary papers on this subject and a general introduction by Remo Ruffini.