The B.X. (Before Xerox) Era
Most people tend to associate the invention of the mouse with Xerox and its research park. In fact, the first functional mouse was actually demonstrated by Douglas Engelbart, a researcher from the Stanford Research Institute, back in 1963. The respective peripheral was far away from what we know today as “mice,” given the fact that it was manufactured from wood and featured two gear-wheels perpendicular to each other, the rotation of each single wheel translating into motion along one of the respective axes.
It's not exactly very clear where the name “mouse” originates, since, apparently, the name came from the fact that the device had a “tail” behind it, connecting it to a computer and a display and was the idea of Bill English, a colleague of Engelbart's and the person who actually built the prototype device.
Engelbart's product was not the first pointing device, though. In fact, it seems that the first such product, the trackball, was invented a lot earlier, namely at some point in 1953, by Tom Cranston, Fred Longstaff and Kenyon Taylor from the Royal Canadian Navy, as part of the secret military project DATAR. The name “trackball” comes from the fact that the respective device actually used a standard Canadian five-pin bowling ball. Just imagine how “easy” using such a product really was.