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The grandfather of Kepler had been the local burgomaster but his father seems to have been a humble soldier away on military service for most of Kepler's early youth. His mother was described by Kepler as “quarrelsome, of a bad disposition.” She was later to be accused of witchcraft. Kepler was born at Würtenburg, in Germany, and was originally intended for the Church; he graduated from the University of Tübingen in 1591 and went on to study in the theological faculty.

In 1594 he was offered a teaching post in mathematics in the seminary at Gratz in Styria. It was from his teacher, Mästlin, who was one of the earliest scholars fully to comprehend and accept the work of Nicolaus Copernicus, that the young Kepler acquired his early Copernicanism. In addition to his teaching at Gratz and such usual duties as mathematicians were expected to do in those days Kepler published his first book – Mysterium cosmographicum (1596; Mystery of Cosmography). The book expresses very clearly the belief in a mathematical harmony underlying the universe, a harmony he was to spend the rest of his life searching for. In this work he tried to show that the universe was structured on the model of Plato's five regular solids. Although the work verges on the cranky and obsessive it shows that Kepler was already searching for some more general mathematical relationship than could be found in Copernicus.

He married in 1597 shortly before he was forced to leave Gratz when, in 1598, all Lutheran teachers and preachers were ordered to leave the city immediately. Fortunately for Kepler, he had an invitation to work with Tycho Brahe who had recently become the Imperial Mathematician in Prague. Tycho was the greatest observational astronomer of the century and he had with him the results of his last 20 years' observations. Kepler joined him in 1600 and although their relationship was not an easy one it was certainly profitable. Tycho assigned him the task of working out the orbit of Mars. Somewhat rashly Kepler boasted he would solve it in a week – it took him eight years of unremitting effort. Not only did Kepler lack the computing assistance now taken for granted but he was also working before the invention of logarithms. It was during this period that he discovered his first two laws and thus, with Galileo, began to offer an alternative physics to that of Aristotle. The first law asserts that planets describe elliptic orbits with the Sun at one focus while the second law asserts that the line joining the Sun to a planet sweeps out equal areas in equal times. The laws were published in his magnum opus Astronomia nova (1610; New Astronomy).

Tycho had died in 1601 leaving Kepler with his post, his observations, and a strong obligation to complete and publish his tables under the patronage of their master, the emperor Rudolph II. This obligation was to prove even more onerous and time consuming than the orbit of Mars. It involved dealing with Tycho's predatory kin, attempting, vainly, to extract money from the emperor to pay for the work, which he ended up financing himself, and trying to find a suitable printer. All this, it must be realized, was done against the background of the Thirty Years' War, marauding soldiery, and numerous epidemics. His work, theTabulae Rudolphinae (Rudolphine Tables), was not completed until 1627 but remained the standard work for the best part of a century.

While serving the emperor in Prague, Kepler had also produced a major work Optics (1604), which included a good approximation of Snell's law, improved refraction tables, and discussion of the pinhole camera. In the same year he observed only the second new star visible to the naked eye since antiquity. He showed, as Tycho had done with the new star of 1572, that it exhibited no parallax and must therefore be situated far beyond the solar system. He studied and wrote upon the bright comet of 1607 – later to be called Halley's comet – and those of 1618 in his Three Tracts on Comets (1619). His final work in Prague, the Dioptrics(1611), has been called the first work of geometrical optics.

In 1611 Kepler's wife and son died, civil war broke out in Prague, and Rudolph was forced to abdicate. Kepler moved to Linz in the following year to take up a post as a mathematics teacher and surveyor. Here he stayed for 14 years. He married again in 1613. While in Linz he produced a work that, starting from the simple problem of measuring the volume of his wine cask, moved on to more general problems of mensuration – Nova stereometria (1615; New Measurements of Volume). One further crisis he had to face was his mother's trial for witchcraft in Würtemburg. The trial dragged on for three years before she was finally freed. His greatest work of this period Harmonices mundi(1619; Harmonics of the World) returns to the search for the underlying mathematical harmony expressed in his first work of 1596. It is here that he stated his third law: the squares of the periods of any two planets are proportional to the cubes of their mean distance from the Sun. After the completion of the Rudolphine tables Kepler took service under a new patron, the Imperial General Wallenstein. He settled at Sagan in Silesia. In return for the horoscopes Wallenstein expected from him, Kepler was provided with a press, a generous salary, and the peace to publish his ephemerides and to prepare his work of science fiction – A Dream, or Astronomy of the Moon (1634). He left Sagan in 1630, during one of Wallenstein's temporary military setbacks, to see the emperor in Ratisbon hoping for a payment of the 12,000 florins still owed him. He died there of a fever a few days later.

As a scientist Kepler is of immense importance. Copernicus was in many ways a traditional thinker, still passionately committed to circles. Kepler broke away from this mode of thought and in so doing posed questions of planetary motion that it took a Newton to answer.