The first computer mouse was built by -

The computer mouse as we know it today was invented and developed by Douglas Engelbart, with the assistance of Bill English, during the 1960s and was patented on November 17, 1970.

While creating the mouse, Douglas was working at the Stanford Research Institute in Menlo Park, California, a think tank sponsored by Stanford University. The mouse was originally referred to as an "X-Y Position Indicator for a Display System" and was first used with the Xerox Alto computer system in 1973.

Source: ComputerHope.com