What is the purely observational evidence used to infer the existence of Dark Matter?

Observations of galaxy rotation curves and gravitational lensing

The evidence supporting the existence of dark matter is entirely gravitational, as the substance does not interact with light. Scientists rely on observations of galaxy rotation curves, which show that stars orbit the galactic center much faster than the visible mass allows for; without additional unseen mass, these galaxies would disperse. Furthermore, gravitational lensing studies reveal massive halos of unseen material surrounding galaxy clusters, demonstrating that gravity is bending light far more than visible matter accounts for. Dark matter's presence is inferred by mapping these substantial gravitational effects.