Newton's Universal Law of Gravitation

Newton's universal law of gravitation is: 

Any object attracts another with a force that is directly proportional to their masses, and inversely proportional to the square of the distance between them. 

An apple falling from a tree accelerates - it starts from rest and picks up speed. By the second of Newton's laws of motion, there must be a force causing the acceleration. Sir Isaac Newton created the idea of this force - the force of gravity. His law of gravitation became universal when he realised that the force causing apples to fall could also act on heavenly bodies.

Johannes Kepler, using Tycho Brahe's calculations,  showed that the planets move in elliptical orbits around the Sun. Newton's universal law of gravitation  predicted that the planets would follow Kepler's elliptical orbits, and allowed astronomers to calculate their positions with great accuracy. Only in the twentieth century were measurements made that showed that Newton's universal law of gravitation gave the wrong positions in extreme circumstances. This resulted in the acceptance of Einstein's general theory of relativity as providing a more accurate theory of gravitation than Newton's universal law of gravitation.

Newton's Universal Law of Gravitation - Equation

Assume an object of mass m, an object of mass M, and a distance between them of r. The force between them is:

F = GMm/r²

where G is the gravitational constant and, in *SI units, its *CODATA value is

G = 6.6742 × 10⁻¹¹ Nm²/kg²

Newton's Universal Law of Gravitation - Further Reading

A Short History of Nearly Everything by Bill Bryson - easy & amusing overview. Only one equation is quoted in the whole book and that is F = GMm/r².
A Brief History of Time by Stephen Hawking - Also easy, but with more detail,  context and authority than Bryson. Also mentions only one equation, not F = GMm/r².
The Road to Reality by Roger Penrose - The most challenging popular physics book, includes F = GMm/r² and thousands of other equations
Big Bang by Simon Singh, p.118. It's a popular account, but he's not afraid to introduce the famous formula: F = GMm/r².