Evidence that galaxies are made of billions of stars? What is the evidence that galaxies are made of billions of stars? 

Even faint galaxies?  

Can spectral analysis distinguish galaxies from individual stars?
The individual stars can be resolved in galaxies close to us...including our own, the Milky Way Galaxy.
More distant galaxies are morphological similar to those that can be resolved into stars, so a natural induction would be that they are similar in nature to those we can resolve into stars.
Galactic spectra are consistent with them being composed of stars in the sort of relative motion we expect.
Supernovae are observed in distant galaxies, and these are similar to those seen close up which we know are stellar in origin.
... etc