Isaac Newton was born in a Lincolnshire hamlet several months after the death of his father. At the time of his birth, the calendar had been changed to its current version in most of Europe but not yet in England; thus, though it was January 4, 1643 by modern reckoning, it was Christmas Day of 1642 in "local time." His mother remarried when he was 3 and left him to be raised by his grandmother while she lived with her husband, returning upon his death when Isaac was 15. In the interim, the boy had been educated at local schools and demonstrated a proficiency for mechanical devices, including water clocks and windmills; he may have invented a four-wheeled carriage pedaled by its rider like a bicycle, but the details are scant.
Newton's mother took him out of school for a time, intending to make a farmer of him, but it quickly became apparent that this was a mistake, and her relatives talked her out of it and sent him back to the grammar school (the equivalent of high school, given his age) in nearby Grantham. An anecdote told by Newton himself illustrates his thirst for knowledge as a boy: having bought a book on astrology, he found parts of it incomprehensible because he didn't know trigonometry; so he bought Euclid's Elements, but discarded it, finding too much of it obvious; and from there, bought Rene Descartes' Geometry, which instilled in him his lifelong love of mathematics. Descartes had integrated the previously separate disciplines of algebra (introduced to Western Europe by the Arabs during their control of Spain) and geometry (part of Western heritage since the Greeks) into analytic geometry, a precursor of the calculus Newton would later develop.
At 18, he was admitted to Trinity College in Cambridge, a bastion of classical thought, though Newton was more interested in the work of more recent natural philosophers like Galileo and Descartes, and had to be talked into reapproaching Euclid. He did advanced work in mathematics at Trinity, and when the college shut down because of the Plague, he worked at home for two years, where he developed -- startlingly -- his theories of gravitation and optics, as well as his calculus.
Newton and Gottfried Leibniz both developed calculus separately, without knowledge of each other; after Descartes' contributions to mathematics, the conditions were simply ripe for the development. It was years, though, before Newton published his calculus. He did publish his work on the generalized binomial theorem, the theory of finite differences, and the logarithmic approximation of partial sums, things which may sound arcane to us outside of math class but which were important in their day. He was appointed Lucasian Professor of Mathematics, the only position at either Cambridge or Oxford which required that its holder devote himself to science rather than the church -- which Newton used to argue that he should be exempt from the usual requirement of being ordained as a priest of the Church of England, a lucky thing given his unorthodox views.
For the early 1670s, his notable work was in optics. He invented an improved telescope, demonstrated the way white light is divided into colored bands by a prism, proposed a corpuscular theory of light (that is, the theory that light is made of particles -- which is half-right) and further proposed the existence of the ether or alchemical forces to explain light's wave-like behavior. In trying to understand lenses and optics, he even cut the lens of his own eye, a dangerous and frankly ridiculous thing to do that is sometimes used as evidence by those historians who think Newton may have suffered from a mild form of autism. Certainly he could be the model of the "absent-minded professor," so focused on his work that reasonable concerns escaped him.
At the end of the decade he worked mostly in mechanics -- a large part of what we'd now call physics, especially the relationship between the planets and between objects. When he published his Philosophiae Naturalis Principia Mathematica in the summer of 1687, he became a celebrity in the scientific and mathematical community. The Principia not only presented his law of universal gravitation, it included his three laws of motion, still studied in many schools today:
The First Law states that an object at rest tends to stay at rest, while at object in motion tends to remain in motion -- the law of inertia.
The Second Law states that an applied force on an object equals the time rate of change of its momentum -- the source of the well-known equation F=ma, Force equals Mass times Acceleration. The unit of measurement of force is the newton now, named in his honor.
The Third Law, perhaps the best known to the layman, states that for every action there is an equal and opposite reaction.
Most people, when they think of Newton and gravity, think of the story of the apple Newton saw fall from a tree (or which hit him on the head). While there's some truth to the story, it's usually misrepresented. He didn't discover gravity (though he was the one to refer to the force by that name), since clearly for all of history, anyone could observe that a fallen object lands on the ground. Instead, Newton's theory dealt with the distance from the Earth at which its gravity still extended -- and the notion that the Earth's gravity was what kept the Moon in orbit.
That was, surprisingly, his last major scientific work. He became involved in the scientific community, served briefly as a member of Parliament (which must have bored him, as there is no record of his contributing to the discussion at all), and wrote a number of religious works dealing with his interpretation of the Bible and especially of Biblical prophecy (Romantic poet William Blake was especially interested in Newton's prophetic analysis), and was given an honorary position at the Royal Mint which he was expected to ignore but instead used to reform England's coin system. It was, in fact, his work at the Mint which earned him his knighthood.
He spent a good deal of time searching for hidden codes in the Bible. His religious writing in fact far outweighed his scientific writing, though even in his own day he was better known as a scientist than a theologian. He believed in a rational universe but not the blind watchmaker of Deism -- God was still active in the world, in Newton's view, and he considered atheism a ridiculous position.
Never good at politics, he alienated as many of his admirers as he accumulated. Some of this may have been the result of ongoing mercury poisoning due to his work in alchemy -- inhalation of mercury fumes causes gradual brain damage, which was instrumental in his death in 1727.