  The Baksan Experiment on Sterile Transitions (BEST) probes the gallium
anomaly and its possible connections to oscillations between active and sterile
neutrinos. Based on the Gallium-Germanium Neutrino Telescope (GGNT) technology
of the SAGE experiment, BEST employs two zones of liquid Ga target to explore
neutrino oscillations on the meter scale. Oscillations on this short scale
could produce deficits in the $^{71}$Ge production rates within the two zones,
as well as a possible rate difference between the zones.
  From July 5th to October 13th 2019, the two-zone target was exposed to a
primarily monoenergetic, 3.4-MCi $^{51}$Cr neutrino source 10 times for a total
of 20 independent $^{71}$Ge extractions from the two Ga targets. The $^{71}$Ge
production rates from the neutrino source were measured from July 2019 to March
2020. At the end of these measurements, the counters were filled with $^{71}$Ge
doped gas and calibrated during November 2020. In this paper, results from the
BEST sterile neutrino oscillation experiment are presented in details. The
ratio of the measured $^{71}$Ge production rates to the predicted rates for the
inner and the outer target volumes are calculated from the known neutrino
capture cross section. Comparable deficits in the measured ratios relative to
predicted values are found for both zones, with the $4 \sigma$ deviations from
unity consistent with the previously reported gallium anomaly. If interpreted
in the context of neutrino oscillations, the deficits give best fit oscillation
parameters of $\Delta m^2=3.3^{+\infty}_{-2.3}$ eV$^2$ and sin$^2
2\theta=0.42^{+0.15}_{-0.17}$, consistent with $\nu_e \rightarrow \nu_s$
oscillations governed by a surprisingly large mixing angle.
