Radiometric tracking data collected by NASA's Deep Space Network (DSN) for Mariner 9, Viking 1 and 2 orbiters, and Mars Global Surveyor (MGS) have been analyzed to determine the gravity field of Mars. The gravity solution (MGS75D) is a complete spherical harmonics model to degree and order 75. Also parts of the solution are the gravitational constants of Mars, Phobos, and Deimos. The significant improvement in the MGS75D Mars gravity model is mainly a consequence of globally distributed data set collected from the MGS mapping orbits, the use of optimal weighting and constrained least squares solution techniques, and improved force and measurement models in the orbit determination process. The gravity anomaly map reveals significantly more detail and larger amplitudes than any previous Mars gravity map over the major impact and volcanic areas on Mars. Olympus Mons remains the largest known gravity anomaly in our solar system and Isidis Planitia, the highest-amplitude mascon. There are mascons in the Hellas, Argyre, and Utopia basins. Valles Marineris has distinctive negative anomalies, and all volcanic features are positive. Gravity anomalies over several craters have also been resolved. The overall correlation of the MGS75D gravity anomaly map with topography derived from the Mars Orbiter Laser Altimeter (MOLA) is very high, while the polar regions display relatively poor correlation.