The temperature-dependent phase diagrams, from 40 to -50 degrees C, of the binary (NH4)(2)SO4/H2O system are derived from data collected in a low-temperature, single-levitated-particle apparatus. The conditions of vapor pressure, temperature, and composition, at which particle phase transitions occur along the path of increasing relative humidity, define the equilibrium phase diagram, whereas the set of conditions that induce transitions in the reverse direction defines the metastability phase diagram. A new, stable crystalline phase of (NH4)(2)SO4. 4H(2)O is identified. Below -19.35 +/- 0.05 degrees C, the anhydrous (NH4)(2)SO4-ice eutectic point, ammonium sulfate does not deliquesce as the RH is increased but instead undergoes a solid-solid phase transition to form a tetrahydrate phase. (NH4)(2)SO4. 4H(2)O incongruently melts at -19.35 degrees C. Equilibrium phase transition, as well as metastable to stable phase transitions, for this system are mapped out, and the derived phase diagrams allow for prediction of the composition and phase of (NH4)(2)SO4 aerosols under the full range of atmospheric conditions and paths. Present observations are in excellent agreement with previous data.