Recordings of the tracking signals received from Voyager 2 during its occultation by Neptune have been used to study the vertical structure of Neptune's atmosphere. The measurements, which began at a planetographic latitude of 62-degrees north and ended near 45-degrees south, cover an altitude interval of about 5000 km. Inversion and interpretation of the occultation data have provided new information on the distribution of free electrons in Neptune's ionosphere, the thermal structure and composition of its troposphere and stratosphere, and the zonal winds below the 1.7 bar level in the troposphere. The 1 bar isobaric surface has equatorial and polar radii of 24 766 +/- 15 km and 24 342 +/- 30 km, respectively, and a corresponding oblateness of 0.0171 +/- 0.0014. At this pressure level, the temperature was 72 +/- 2 K. The tropopause was detected approximately 40 km above the 1 bar level at a pressure of about 100 mbar. A comparison with infrared observations indicates that the gas at the tropopause consists of 78%-84% hydrogen by number density with the rest being mostly helium. The temperature in this region was 52 +/- 2 K. Above the tropopause, the temperature is increasing with altitude reaching 130 +/- 12 K near the 0.3 mbar level. A 2-3 km thick layer with a small refractivity scale height whose top was detected 14 km below the 1 bar level, may be a region where the CH4 mixing ratio is decreasing rapidly with increasing altitude-perhaps as a result of vapor condensation effects that produce haze. For the nominal model derived from the ingress measurements, this interpretation yielded a CH4 mixing ratio of 2% at the base of the layer where the pressure was about 1.9 bars. Uncertainties in the atmospheric rotation period affect the interpretation of the measurements below the 1.7 bar level. A rotation period of 14.2 +/- 0.3 hr was found to be consistent with the ingress data acquired at 60-degrees north latitude, and was adopted for the nominal model. This rotation period corresponds to an eastward zonal wind velocity of 176 +/- 32 m/s relative to the magnetic field. Data acquired between 38-degrees and 15-degrees south during egress indicate westward zonal winds with velocities ranging from 100 to 400 m/s below the 1.7 bar level. Ammonia vapor was assumed to be the principal microwave absorber limiting the depth of the measurements in the troposphere. At the lowest level where the link was detected during ingress, the nominal model has a pressure and temperature of 6.3 bars and 135 K, respectively. The ammonia mixing ratio at this level was 500 +/- 150 parts per billion.