The four large inner moons of Jupiter were discovered by Galileo Galilei, in January of 1610. As a result, they are often referred to as the Galilean satellites.
Aside from their common discovery, the moons are closely linked by gravitational interactions with each other and Jupiter. Their mutual interactions cause them to have almost exactly commensurate orbits -- that is, the orbital period of each moon is closely linked to that of its neighboring companions, according to the ratio of two small whole numbers. Thus, the orbital period of Europa is almost exactly twice (2/1) that of Io, the orbital period of Ganymede is almost exactly twice that of Europa, and the orbital period of Callisto is almost exactly 7/3 that of Ganymede. This sort of regularity is very common in the Solar System, being found in satellite systems (as noted here), in the spacing of the planets, in the spacing of gaps in the rings of Saturn, and in the "Kirkwood gaps" in the asteroid belt (see the second half of Orbital Regularities).
In addition, the mutual orbital interactions of the moonscause small perturbations (changes) in their orbits, which cause their tidal interaction with Jupiter's gravitational field to flex their surfaces and interiors -- stretching and shrinking them along the line between the planet and a given satellite -- and in the process, generating substantial heat inside the inner moons, and lesser amounts in the more distant ones. In the case of Io, the flexure is almost a mile, and the heating produced in this way has almost completely melted the rocky interior of the moon, making it the most volcanically active object in the Solar System. For Europa, the flexing is much less, but the heat appears to have been adequate to melt a substantial part of its icy interior, causing the cracked and crazed appearance of its surface layers. For Ganymede and Callisto, the tidal heating is too small to produce substantial effects, but the steady decrease of geological activity with increasing distance from Jupiter continues, with Ganymede being strongly differentiated, and having large surface areas altered by geological activity within the last four billion years, while Callisto is apparently undifferentiated, and has little evidence of activity since the period of heavy bombardment ended four billion years ago, leaving it one of the most totally cratered objects in the Solar System.