From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
Doctor Mu (ドクター ミュー, Dokutā Myū; FUNimation "Dr. Myuu") is a brilliant scientist who desires nothing more than total control of the universe.
Black Star Dragon Ball Saga - Baby Saga
Mu masterminds the plot to build an ultimate Machine Mutant out of Trunks Brief, Son Pan, and Son Goku to see his sinister goal of control through to the end. To this end, he created a powerful enforcer named Rild, and tried to gather the Black Star Dragon Balls to use them to complete his creation, Baby, and use it to take over the universe. However, Goku, Pan, and Trunks got past Rild and foiled Mu's plans. Mu escaped but was killed when Baby burst out of his body. It was revealed that Baby was actually the one who programmed Mu, and not the other way around.
Super 17 Saga
Mu later teamed up with Doctor Gero in Hell and created a Machine Mutant duplicate of No. 17, who controlled the original Artificial Human No. 17 and converged their powers together to set a rift between Planet Earth and Hell. Hell Fighter No. 17 and the two scientists escaped, following which the two No. 17s eventually fused together to become Super No. 17. Super 17 betrayed and killed Gero thanks to Mu's programming changes and then went on to dominate the Z Warriors (including Super Saiyan 4 Goku thanks to his absorption field ability) to the point that Mu truly believed he could take over the universe until Artificial Human No. 18 showed up and got in his head by appealing to his sense of self.
Mu, in anger at No. 18's apparent influence, ordered Super No. 17 to destroy Goku and No. 18 with his Electro Eclipse Bomb attack so as to show them "who he really is" and that he "can't be manipulated or controlled". Super No. 17 turned on Mu, however, the very man who had been using him the entire time, and destroyed him with the attack. He was sent back to Hell after this.
- In the FUNimation dub, Mu speaks with a German accent and says such words as "Guten tag", a phrase in German which means "Good day" or "Good afternoon".
- Mu shares somewhat of a resemblance with Dr. Lychee and Gero, which may or may not be coincidental.
- Mu and Gero are very similar in appearance and design (ex: mustache, long hair, and tall hat). Also, both Mu and Gero are killed by their own creations (the Androids and Baby, though the latter was technically his master, as he was created by Baby). Additionally, Mu and Gero met their final fates by a shared creation, Super 17.