Jupiter is the gas giant with the most moons in the Sol system. While it is definitely confirmed that there are larger gas giants in the Milky Way Galaxy, telling how many moons they might have is not a possibility yet. To this end, the 5th and largest planet from the Sun has a current total of 64 moons, with some waiting to be confirmed and new discoveries possible.
Jupiter is a gravity well due to its status as the largest object in the solar system other than the Sun, so it is the most likely object to capture material entering the system, from the Kuiper Belt or beyond. This reality is why Jupiter will likely always be the object the most moons, even though Saturn is close in total number, barring some catastrophe in the future.
Among these are the 4 largest terrestrial moons, called the Galilean moons, as they were discovered by the famous scientist Galileo. These are Io, Europa, Ganymede, and Callisto. They all formed at the same time as Jupiter, based on their orbits. Europa is of particular interest due to the presence of icy crust unblemished by craters, suggesting that a liquid ocean exists beneath, kept liquid by tidal heating, and the possibilities for life to exist are intriguing as well.