The first mathematical formulation of gravity was published in 1687 by Sir Isaac Newton. His law of universal gravitation was the standard theory of gravity until work by Albert Einstein and others on general relativity. Since calculations in general relativity are complicated, and Newtonian gravity is sufficiently accurate for most applications, when dealing with weak gravitational fields (e.g., when launching rockets, projectiles, or swinging pendulums, etc.), Newton's formulas are generally preferred.
Steven Weinberg noted that we could still build a suspension bridge with Newton's laws. Newton's theory is much simpler in mathematical structure than general relativity, and is used very often. Newton's Laws are generally taught at the high school level while general relativity is taught only to students opting for physics in undergraduate and graduate courses.
Quantum gravity is the attempt to unify the theories of Gravitation and Quantum mechanics in a self-consistent manner, or more precisely, to formulate a self-consistent theory which reduces to ordinary quantum mechanics in the limit of weak gravity (potentials much less than c2) and which reduces to Einsteinian general relativity in the limit of large actions.