Newton's First Law: "Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed on it."
Newton's Second Law: "The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed."
This is often summarized in the equation:
Newton's Third Law: "To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." or more commonly "For every action force, there is an equal and opposite reaction force".
Using Newton's laws
Much of classical mechanics is derived from Newton's second law, particularly calculations involving momentum and acceleration.
When solving problems, a useful way restate the third law is, "Forces always come in equal pairs."
It is important to realise that the reaction force always acts on a different body to the initial force. If body A exerts a force on body B, then body B exerts an equal force on body A. The reaction force has the same line of action, and is of the same type and magnitude as the original force.
Newton first gave his laws in the first volume of his Philosophiae Naturalis Principia Mathematica in 1687 and, using the mathematical tools of his newly developed calculus, proved many results concerning the motion of idealised particles. In the third volume, he showed how, combined with his law of universal gravitation, his laws of motion explained the motion of the planets and the Laws of Kepler. Not until 1916 and Albert Einstein's theory of relativity did anyone improve upon Newton's model of the motions of the planets.