There are known to be at least 67 moons of Jupiter. A list of the 67 known moons can be seen on Wikipedia page the Moons of Jupiter.
The 4 largest, seen in 1609 by Galileo, are Io, Europa, Ganymede and Callisto – they are known as the Galilean moons. There are less detailed reports of earlier observations, by the Chinese, of the moons dating back to the 4th century BC. More details of the Galilean moons are given on the Wikipedia links beneath the following images: