Kepler's first book, the Mysterium Cosmographicum of 1596, argued that the spacing of the six known planets was fixed by the five regular solids nested between their spheres. The scheme is wrong. The conviction behind it he never abandoned: that the heavens are ordered by exact ratios, and that the ratios can be found.
The work that made him was done on Tycho Brahe's observations of Mars, the most accurate then in existence. He spent years trying to fit them to circles and failed by an amount, eight minutes of arc, small enough that almost any other astronomer would have set it aside. He did not, and the Astronomia Nova of 1609 states the result: a planet moves on an ellipse with the sun at one focus, and the line from sun to planet sweeps equal areas in equal times. The second of those broke the assumption of uniform circular motion that astronomy had held since antiquity.
The Harmonices Mundi of 1619 is where the search for ratios pays twice. It contains the third law, relating a planet's period to its distance, set inside a book largely concerned with musical consonance, polyhedra and the harmonies he believed the planetary motions sound. He then compiled the Rudolphine Tables, published in 1627 on Tycho's data and his own theory, which made the new astronomy usable for prediction and settled the practical argument in its favour long before the physical one was won.