The Zwicky Transient Facility (ZTF), a public-private enterprise, is a new time domain survey employing a dedicated camera on the Palomar 48-inch Schmidt telescope with a 47 deg$^2$ field of view and 8 second readout time. It is well positioned in the development of time domain astronomy, offering operations at 10% of the scale and style of the Large Synoptic Survey Telescope (LSST) with a single 1-m class survey telescope. The public surveys will cover the observable northern sky every three nights in g and r filters and the visible Galactic plane every night in g and r. Alerts generated by these surveys are sent in real time to brokers. A consortium of universities which provided funding ( arcsecpartnership arcsec) are undertaking several boutique surveys. The combination of these surveys producing one million alerts per night allows for exploration of transient and variable astrophysical phenomena brighter than r $sim$ 20.5 on timescales of minutes to years. We describe the primary science objectives driving ZTF including the physics of supernovae and relativistic explosions, multi-messenger astrophysics, supernova cosmology, active galactic nuclei and tidal disruption events, stellar variability, and Solar System objects.