Galileo first observed the phases of Venus in 1610.
Using his improved telescope, Galileo observed Venus displaying a complete sequence of phases, from crescent to gibbous and nearly full, near the end of 1610. He did not publish the observations immediately; they appeared later in his 1613 work Letters on Sunspots.
The phases were powerful evidence against the traditional Ptolemaic system. In that model, Venus remained between Earth and the Sun and could not show a fully illuminated disk. The observations were compatible with the Copernican system, in which Venus orbits the Sun, and also with Tycho Brahe’s geo-heliocentric model.
There is a historical dispute over who first noticed the phases. In December 1610, Galileo received a letter from Benedetto Castelli asking whether his telescope could reveal them. Galileo soon told Johannes Kepler that he had observed the phases, but surviving evidence does not completely establish whether Castelli was reporting an independent observation or responding to Galileo’s earlier information. The year 1610 nevertheless remains the standard answer.