Newton was born in Woolsthorpe-by-Colsterworth (at Woolsthorpe Manor), a hamlet in the county of Lincolnshire. Newton was born prematurely, and no one expected him to live; indeed, his mother, Hannah Ayscough Newton, is reported to have said that his body at that time could have fit inside a quart mug (Bell, 1937). His father, Isaac, had died three months before Newton's birth. When Newton was two, his mother went to live with her new husband, leaving her son in the care of his grandmother.

According to E.T. Bell (1937, Simon and Schuster) and H. Eves:

Newton began his schooling in the village schools and was later sent to The Kings Grammar School (Grantham) where he became the top boy in the school. At Kings he lodged with the local apothecary, William Clarke and eventually became engaged to the apothecary's stepdaughter, Anne Storer, before he went off to Cambridge University at the age of 19. As Newton became engrossed in his studies, the romance cooled and Miss Storer married someone else. It is said he kept a warm memory of this love, but Newton had no other recorded 'sweethearts' and never married.

However, William Stukeley and Mrs Vincent, the source which Bell and Eves have embroidered so unhelpfully, merely say that Newton entertained 'a passion' for her while he lodged at the Clarke house. Mrs Vincent's maiden name was Katherine Storer, not Anne.

From the age of about twelve until he was seventeen, Newton was educated at The King's School in Grantham (where his signature can still be seen upon a library window sill). He was removed from school and by Oct 1659 he was to be found at Woolsthorpe where his mother attempted to make a farmer of him. He was, by later reports of his contemporaries, thoroughly unhappy with the work. It appears to be Henry Stokes, master at the King's School, who persuaded his mother to send him back to school so that he might complete his education. This he did at the age of eighteen, achieving an admirable final report. His teacher said:

His genius now begins to mount upwards apace and shine out with more strength. He excels particularly in making verses. In everything he undertakes, he discovers an application equal to the pregnancy of his parts and exceeds even the most sanguine expectations I have conceived of him.

In June 1661 he matriculated to Trinity College, Cambridge. At that time, the college's teachings were based on those of Aristotle, but Newton preferred to read the more advanced ideas of modern philosophers such as Descartes and astronomers such as Galileo, Copernicus and Kepler. In 1665 he discovered the generalized binomial theorem and began to develop a mathematical theory that would later become calculus. Soon after Newton had obtained his degree in 1665, the University closed down as a precaution against the Great Plague. For the next 18 months Newton worked at home on calculus, optics and law of gravitation. Newton was a strange character, often not sharing information he had discovered unless he was asked. Calculus for example, was something he had invented 30 years before he had told anyone else about it.

Mathematical research
Newton became a fellow of Trinity College in 1669. In the same year he circulated his findings in De Analysi per Aequationes Numeri Terminorum Infinitas (On Analysis by Infinite Series) , and later in De methodis serierum et fluxionum (On the Methods of Series and Fluxions), whose title gave rise to the "method of fluxions".
Optics
From 1670 to 1672 he lectured on   optics . During this period he investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light. He also showed that the coloured light does not change its properties, by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus the colours we observe are the result of how objects interact with the incident already-coloured light, not the result of objects generating the colour. For more details, see Newton's theory of colour. Many of his findings in this field were criticized by later theorists, the most well-known being Johann Wolfgang von Goethe, who postulated his own colour theories.
Gravity and motion
In 1679, Newton returned to his work on mechanics, i.e., gravitation and its effect on the orbits of planets, with reference to Kepler's laws of motion, and consulting with Hooke and Flamsteed on the subject. He published his results in De Motu Corporum (1684). This contained the beginnings of the laws of motion that would inform the Principia.

The Philosophiae Naturalis Principia Mathematica (now known as the Principia) was published on 5 July 16871 with encouragement and financial help from Edmond Halley. In this work Newton stated the three universal laws of motion that were not to be improved upon for more than two hundred years. He used the Latin word gravitas (weight) for the force that would become known as gravity, and defined the law of universal gravitation. In the same work he presented the first analytical determination, based on Boyle's law, of the speed of sound in air.

With the   Principia, Newton became internationally recognised. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed an intense relationship that lasted until 1693. The end of this friendship led Newton to a nervous breakdown.