Dark matter was first postulated as a result of [Vera Ruben][1]'s observations of galaxies' rotation curves, which were flat ($\color{green}{\mathrm{green}}$ in the diagram below), showing that stars revolve much faster than expected based upon Newtonian mechanics ($\color{red}{\mathrm{red}}$ in the diagram below):

[![Observed vs. Predicted Galaxy Rotation Curve][2]][3]
Dark matter postulate: Explains why there is much more mass in galaxies than the mass that emits light

Alternative theories of gravity ([Modified Newtonian Dynamics (MOND)][4], [Weber's gravitational force][5], etc.): Explains galaxy rotation curves assuming we can "weigh" galaxies accurately based upon the light they emit.

  [1]: https://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/vera-cooper-rubin
  [2]: https://i.sstatic.net/Eqmyq.gif
  [3]: http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit6/dark.html
  [4]: http://www.scholarpedia.org/article/The_MOND_paradigm_of_modified_dynamics
  [5]: http://www.ifi.unicamp.br/~assis/Relational-Mechanics-Mach-Weber.pdf