We report on novel ferromagnetic Mn/Ge multilayers for spintronics applications investigated both experimentally and theoretically. Two Mn/Ge multilayers are grown on GaAs (001) substrates by molecular beam epitaxy. The period of each multilayer consists of an Mn layer of varying thickness (0.6 and 5 Å) and a 10 Å thick Ge spacer layer. From temperature-dependent magnetization and hysteresis loop measurements, the Mn (0.6 Å)/Ge (10 Å) multilayer showed very weak ferromagnetic ordering, which is persistent up to 260 K, whereas the Mn (5 Å)/Ge (10 Å) multilayer exhibited strong ferromagnetism up to 305 K. The coercive field of the Mn (5 Å)/Ge (10 Å) multilayer was 277 Oe at 200 K. Density functional electronic band structure calculations on a number of Mn/Ge (001) multilayers determined them to be ferromagnetic, and estimates of their critical temperatures are reported.