Kernel
Galileo is the figure who turns Italian instrument-making into experimental physics. He builds his own telescope (improving on Dutch designs), discovers Jupiter's moons in 1610 — a direct empirical refutation of the Aristotelian geocentric model — formulates the law of free fall, the principle of relativity in mechanics, and writes Two New Sciences (1638), the founding text of modern physics. Patronage from the Medici and condemnation by the Inquisition (1633) make him the archetype of the scientist confronting institutional power.
Contribution
The first systematic use of mathematics to describe terrestrial motion. The law of falling bodies. The discovery of Jupiter's moons, the phases of Venus, sunspots, and lunar craters. The mathematical principle of relativity that Newton extends and Einstein generalizes. The very methodology of "do the experiment first."
Lineage
Studied at Pisa; appointed by the Medici to Florence; corresponded with Kepler. His mechanics is the direct precondition for Newton: when Newton says he stands on the shoulders of giants, Galileo is the first giant on the list.
Civilization-scale significance
The figure in whom the church-vs-science conflict first becomes legible to modernity. Also the figure whose specific results most directly produced Newton.