The "cosmic dawn" refers to the period of the Universe's history when stars
and black holes first formed and began heating and ionizing hydrogen in the
intergalactic medium (IGM). Though exceedingly difficult to detect directly,
the first stars and black holes can be constrained indirectly through
measurements of the cosmic 21-cm background, which traces the ionization state
and temperature of intergalactic hydrogen gas. In this white paper, we focus on
the science case for such observations, in particular those targeting redshifts
z $\gtrsim$ 10 when the IGM is expected to be mostly neutral. 21-cm
observations provide a unique window into this epoch and are thus critical to
advancing first star and black hole science in the next decade.