  We present a detailed study of the color magnitude diagram (CMD) of the dwarf
spheroidal galaxy Leo I, based on archival Hubble Space Telescope data. Our
photometric analysis, confirming previous results on the brighter portion of
the CMD, allow us to obtain an accurate sampling of the stellar populations
also at the faint magnitudes corresponding to the Main Sequence. By adopting a
homogeneous and consistent theoretical scenario for both hydrogen and central
helium-burning evolutionary phases, the various features observed in the CMD
are interpreted and reliable estimations for both the distance modulus and the
age(s) for the main stellar components of Leo I are derived. More in details,
from the upper luminosity of the Red Giant Branch and the lower luminosity of
the Subgiant Branch we simultaneously constrain the galaxy distance and the age
of the oldest stellar population in Leo I. In this way we obtain a distance
modulus (m-M)_V=22.00$\pm$0.15 mag and an age of 10--15 Gyr or 9--13 Gyr,
adopting a metallicity Z=0.0001 and 0.0004, respectively. The reliability of
this distance modulus has been tested by comparing the observed distribution of
the Leo I anomalous Cepheids in the period-magnitude diagram with the predicted
boundaries of the instability strip, as given by convective pulsating models.
