Abstract: The Supernova / Acceleration Probe (SNAP) is a proposed space-based experiment designed to measure the expansion history of the Universe, motivated by the discovery that the expansion is accelerating. It will study both the dark energy and the dark matter, through mapping the distance-redshift relation of Type Ia supernovae and through a wide-area weak gravitational lensing survey. The resulting data set can not only determine the amount of dark energy with high precision, but test the nature of the dark energy by examining its equation of state. In particular, dark energy due to a cosmological constant or various classes of dynamical scalar fields can be differentiated.