A cooling jacket of an electric motor or generator includes a cylindrical inner sleeve, a cylindrical outer sleeve coaxially surrounding the inner sleeve and forming a circular space between the outer sleeve and the inner sleeve, and a passageway extending within the circular space between the outer sleeve and the inner sleeve. The passageway may be a continuous winding path that may extend axially back and forth along the circumference of said inner sleeve. An embodiment of the present invention provides a cooling jacket that is suitable for, but not limited to, applications in the aircraft and aerospace industries, for example in air-conditioning systems. The cooling jacket as in one embodiment of the present invention may be leak proof and water tight, has a compact design, and may be easily assembled and integrated into an electrically driven machine, such as an electrically driven compressor.