There is no object in the Universe that does not rotate on its axis and our Milky Way is no exception. This vast system of stars, shaped like a flattened disc, is a spiral, with stars, dust and gas clouds visibly concentrated along enormous spiral arms which curve away from the galactic center to its edge.
The whole system is rotating, but not like a solid body. Gravity makes its inner regions swirl around far more rapidly than those parts as far out as the Sun, so that a star in an inner orbit will do a lap in only a few thousand years — a trip which takes our Sun 250 million years to complete, even though it is travelling at almost 1 million kilometers per hour! The net result of this differential rotation should be to wind up the spiral pattern after just a few revolutions, but this clearly hasn’t happened. Nor do any of the million of other spiral galaxies how any signs of being wound up. One of the biggest puzzles facing astronomers today is to explain how spiral galaxies keep their shape.
Milky Way (Wikipedia)