Includes bibliographical references and index.

pt. I. John Archibald Wheeler and general relativity. John Wheeler and the recertification of general relativity as true physics ; John Archibald Wheeler: a few highlights of his contributions to physics ; Wheeler wormholes and the modern astrophysics -- pt. II. Foundations and tests of general relativity. Unified form of the initial value conditions ; The confrontation between general relativity and experiment ; Measurements of space curvature by solar mass ; Modern cosmology: early and late universe -- pt. III. Gravitational waves. Introduction to gravitational waves ; Discovering relic gravitational waves in cosmic microwave background radiation ; Status of gravitational wave detection ; Search for gravitational waves with resonant detectors ; Gravitational fields with 2-dimensional killing leaves and the gravitational interaction of light -- pt. IV. Frame dragging and gravitomagnetism. Rotation and spin in physics ; The gravitomagnetic influence on Earth-orbiting spacecrafts and on the lunar orbit ; Quasi-inertial coordinates ; Gravitomagnetism and its measurement with laser ranging to the LAGEOS satellites and GRACE Earth gravity models ; The relativity mission gravity probe b, testing Einstein's universe ; The LARES space experiment: LARES orbit, error analysis and satellite structure ; The history of the so-called Lense-Thirring effect, and of related effects -- pt. V. Miscellaneous. Atom interferometers and optical clocks: new quantum sensors based on ultracold atoms for gravitational tests in Earth laboratories and in space ; The York map and the role of non-inertial frames in the geometrical view of the gravitational field.