We create the first large-scale mock spectroscopic survey of gas absorption sightlines traversing the interstellar medium (ISM), circumgalactic medium (CGM), and intergalactic medium (IGM) surrounding galaxies of virtual Universes. That is, we create mock, or synthetic, absorption spectra by drawing lines-of-sight through cosmological hydrodynamical simulations, using a new mesh-free Voronoi ray-tracing algorithm. The result is the Synthetic Absorption Line Spectral Almanac (SALSA), which is publicly released on a feature-rich online science platform (www.tng-project.org/spectra). It spans a range of ions, transitions, instruments, observational characteristics, assumptions, redshifts, and simulations. These include, but are not limited to: (ions) HI, OI, CI, MgI, MgII, FeII, SiII, CaII, ZnII, SiIII, SiIV, NV, CII, CIV, OVI; (instruments) SDSS-BOSS, KECK-HIRES, UVES, COS, DESI, 4MOST, WEAVE, XSHOOTER; (model choices) with/without dust depletion, noise, quasar continua, foregrounds; (redshift) from z=0 to z~6; (ancillary data) integrated equivalent widths, column densities, distances and properties of nearby galaxies; (simulations) IllustrisTNG including TNG50, TNG-Cluster, EAGLE, and SIMBA. We also provide line-of-sight integrals, including Faraday rotation measure (RM) probing magnetic fields, and dispersion measure (DM) as traced by fast radio bursts (FRBs). This scope is not fixed, and will grow and evolve with community interest and requests over time. The resulting dataset is generic and broadly applicable, enabling diverse science goals such as: (i) studies of the underlying physical gas structures giving rise to particular absorption signatures, (ii) galaxy-absorber and halo-absorber correlations, (iii) virtual surveys and survey strategy optimization, (iv) stacking experiments and the identification of faint absorption features, (v) assessment of data reduction methods and completeness calculations, (vi) inference of physical properties from observables, and (vii) apples-to-apples comparisons between simulations and data.
