Professional Work
       Newton's professional work can be summed up in the following categories:

Optics:
In 1664, while still a student, Newton started reading works on optics written by other English physicists, Robert Hooke and Robert Boyle.  He was very interested in this subject and so he started to investigate the refraction of light by a glass prism; developing a series of increasingly elaborate experiments.  By conducting these experiments, Newton discovered that white light is a mixture of infinitely varied coloured rays, each ray is definable by the angle at which it enters or leaves the prism (or any other medium) and also there exists mathematical patterns in the colours of light.  When he first expressed his findings nobody believed him, he was criticized because before Newton's findings, colour was thought to be modified forms of white light.  Newton expressed his finding in Opticks, written in 1692, but waited to publicize it until all the critics were dead.  The book was imperfect, but still served as a model of theory with quantitative experimentation.

Mathematics:
Newton made considerable contributions to all areas of math, but his more famous contributions were in analytical geometry and calculus.  He discovered differentiation (lines tangent to curves) and integration (area underneath a curve) and found that they are inverse of each other.  He also found ways to resolve problems of curvature by a method of fluxions.  He used the term fluxion because he thought of a quantity flowing from one value to another.  Newton's work on math wasn't publicized until 1704.  Newton wasn't alone in finding these "discoveries," Leibniz claimed he independently came up with the first ideas about differential calculus.  This sprung up a huge fight between both men which didn't end even upon Leibniz's death.  Today they are jointly ascribed in the honor of first inventing calculus.


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Universal Law of Gravitation:
According to the well-known story of Newton seeing an apple fall from a tree, Newton conceived that the force on the moon must be the same as the force on the apple.  He calculated the force that it takes to hold the moon in orbit and then compared it to the force pulling the apple to the ground.  He also calculated the centripetal force needed to hold a stone in a sling as well as the relationship between the length of a pendulum and the time of its swing.  Through corresponding with Hooke (another physicist/mathematition) Newton corrected some of the problems he ran into.  And from this he came up with an equation and explanation of gravitational force. 
F=G* (m1 * m2)/r^2
This equation states that every object in the universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects.
This principle was published into a book Principia, which isn't only Newton's masterpiece, but it is also the fundamental work that modern science is built on.  The book was separated into three volumes.  The first stated the foundations of the science of mechanics while mathematically developing them, also gravity was stated in this book as the cause of controlling the motions of celestial bodies.  Book two examines the theory of fluids, while book three shoes the law of gravitation at work in the universe.

Laws of Motion:
The Principia rested on Newton's three laws of motion:
1.   A body remains in its state of rest unless it is compelled to change that state by a force impressed on it.
2.   The change of motion (change in velocity multiplied by the mass) is proportional to the force impressed.
3.   That every action has an equal and opposite reaction.