We present the STARS library, a grid of tidal disruption event (TDE) simulations interpolated to provide the mass fallback rate (dM/dt) to the black hole for a main-sequence star of any stellar mass, stellar age, and impact parameter. We use a one-dimensional stellar evolution code to construct stars with accurate stellar structures and chemical abundances, then perform tidal disruption simulations in a three-dimensional adaptive-mesh hydrodynamics code with a Helmholtz equation of state, in unprecedented resolution: from 131 to 524 cells across the diameter of the star. The interpolated library of fallback rates is available on GitHub (github.com/jamielaw-smith/STARS_library) and version 1.0.0 is archived on Zenodo; one can query the library for any stellar mass, stellar age, and impact parameter. We provide new fitting formulae for important disruption quantities (beta(crit), Delta M, (M) overd dot(peak), t(peak), n(infinity)) as a function of stellar mass, stellar age, and impact parameter. Each of these quantities varies significantly with stellar mass and stellar age, but we are able to reduce all of our simulations to a single relationship that depends only on stellar structure, characterized by a single parameter rho(c)/(rho) over bar, and impact parameter beta. We also find that, in general, more centrally concentrated stars have steeper dM/dt rise slopes and shallower decay slopes. For the same Delta M, the dM/dt shape varies significantly with stellar mass, promising the potential determination of stellar properties from the TDE light curve alone. The dM/dt shape depends strongly on stellar structure and to a certain extent stellar mass, meaning that fitting TDEs using this library offers a better opportunity to determine the nature of the disrupted star and the black hole.