Three years later, he began teaching math and astronomy at the University of Gratz in Austria. During that time, he developed the idea that the universe is governed by geometric relationships from inscribed and circumscribed circles of five polygons - tetrahedron, cube, octahedron, dodecahedron, and icosahedron. He published a book on his findings (in Mysterium Cosmographicum) in 1596, which caught the eye of Tycho Brahe, a renowned Danish astronomer. In 1600, Brahe invited Kepler to Prague to become his assistant. When Brahe died the following year, Kepler was appointed his successor, which gave him complete access to the detailed astronomical data Brahe had compiled during his studies of the universe. Kepler specifically studied the orbit of Mars and proved that the orbit was indeed an ellipse with the Sun located at one of the foci. This discovery led to the first of three laws Kepler developed - commonly known as Kepler's Laws of Planetary Motion.

Kepler also did research in the field of optics. He published a book on optics in 1604 that contained theories on vision and the internal structure of the human eye. As a result, people had a greater understanding why eyeglasses were appropriate for correcting near-sightedness and far-sightedness.

He continued to publish papers on various topics in astronomy and optics until his untimely death in 1630.