The Umayyad Dynasty
The Umayyad family established a system of hereditary succession for the leader of the Muslim world. Mu'awiya assumed this position for the first 20 years of the Dynasty's rule. Under the Umayyads, the Islamic Empire spread to North Africa, Spain and central Asia (left.)
The majority of this new empire was of course non-Muslim, and aside from a protection tax (jizya) the conquered people found their religions tolerated. Nonetheless the new religion penetrated deeply, to the point where conversions were discouraged since they might have been motivated by avoiding taxes, rather than true belief, and choosing a religion should override such economic concerns.
At the same time the Umayyads had dedicated their prestige to conquering the Byzantine empire, and started running into real opposition from the Orthodox provinces. Thus there was a revolution in 750, and a new dynasty, the Abbasids, took the caliphate, marking the transition to a more settled empire and a, disputed, golden age.