The Initial Star formation and Lifetimes of Andromeda Satellites (ISLAndS) project employs Hubble Space Telescope imaging to study a representative sample of six Andromeda dSph satellite companion galaxies. Our main goal is to determine whether the star formation histories (SFHs) of the Andromeda dSph satellites demonstrate significant statistical differences from those of the Milky Way (MW). Our deep observations yield a time resolution at the oldest ages of ∼1 Gyr, allowing meaningful comparisons to the MW satellites. The six dSphs present a variety of SFHs (e.g., a significant range in quenching times, {τ }q, from 9 to 6 Gyr ago) that are not strictly correlated with luminosity or present distance from M31. In agreement with observations of MW companions of similar mass, there is no evidence of complete quenching of star formation by the cosmic UV background responsible for reionization, but the possibility of a degree of quenching at reionization cannot be ruled out. We do not find significant differences between the SFHs of the members and non-members of the vast, thin plane of satellites. The SFHs of the ISLAndS M31 dSphs appear to be more uniform than those of the MW dSphs. Specifically, the primary difference between the SFHs of the ISLAndS dSphs and MW dSph companions of similar luminosities and host distances is the absence of late-quenching ({τ }q≤slant 5 {Gyr}) dSphs in the ISLAndS sample. Thus, models that can produce satellite populations with and without late-quenching satellites are of extreme interest. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs #13028, 13739.