Observations of the X-ray binary system Her X-1 by the AstroSat Soft X-ray Telescope 1 (SXT) were carried out in 2020 through 2023 with the goals of measuring X-ray spectrum changes with the 35-day disk rotation phase and measuring eclipses at different 35-day phases. The four multi-day long observations were scheduled during: turn-on to Main High (MH) and MH rise; MH state; Short High (SH) state; and Low State (LS). 35-day phase was determined using monitoring observations with the Swift Burst Alert Telescope (BAT). Nine eclipses were observed at a range of 35-day phases, with at least one eclipse during each observation. Data with dips were separated from data without dips. The variation of X-ray spectral parameters vs. 35-day phase shows the following: eclipse parameters are nearly constant, showing that the scattering corona does not change with 35-day phase; dips show an increase in covering fraction but not column density compared to non-dip data; the 1 keV line normalization indicates an origin in a small region near the continuum emission region, likely the magnetospheric accretion flow from the inner disk onto the neutron star; and the change in blackbody normalization (area) shows that the emission region is much larger than the 1 keV emission region, and consistent with the inner edge of the accretion disk.