The term galactic archaeology is used for studies of stars and galaxies that reveal the galaxy's history. The Milky Way and nearby galaxies such as the Magellanic clouds offer the most access to detail for such study, from spectrography regarding spectral classes, metallicity, and radial velocity of stars, and from astrometry for peculiar velocities and parallaxes, along with demographics of these characteristics to reveal patterns suggesting groups of stars with a similar history. The ideal product is reasonable concepts of the Milky Way and nearby galaxies as they were millions and billions of years in the past.
Note alternate spelling of archaeology, without the second "a", i.e., archeology. Spelling authorities are split regarding its acceptability, and astrophysics literature has examples of both spellings.