Caliph  The "successor" who became leader of the Islamic community (the Umma) after the death of Muhammad. It also can be defined as "deputy of God" which gives it a "semi-divine" quality.

Caliphate  A  government based on the rule/control by the "successor" after Muhammad's death. Different points of view developed as to who should be the caliph. One view (the Sunni) was that community consensus should determine the caliph. The Shia view was that the Caliph should be descended from a blood relative of Muhammad.

The "rightly guided caliphs" The first four Caliphs after Muhammad during the period 632-661 AD (CE). Abu Bakr (632-634) AD (CE) Omar (634-644) AD (CE) Othman (644-656) AD (CE) Ali (656-661) AD (CE)

Umayyad Caliphate  661-750 AD (CE) Centered in Damascus, Syria expanded the reach of the Arabs and Islam against the Byzantine Empire, the Persian Sassanid (Sassanian) Empire, into central Asia, northern Africa, and into Spain and France in western Europe. In the eight century, the Umayyads suffered significant military defeats at the hands of the Byzantines in 717 AD (CE) and in France at Tours in 732 AD (CE). 

Berbers  Peoples of northern Africa who originally resisted Umayyad expansion but who eventually were converted and assimilated. In 711 AD (CE) they invaded southern Spain conquering the Visigothic Kingdom.

Gibraltar  The mountain or rock of Tariq which was captured by the Berber invaders of Spain in 711 AD (CE). 

Tours  The battle in France 732 AD (CE) during which the Frankish commander Charles Martel ("The Hammer") defeated Islamic forces just north of Poitiers. This marked the furthest reach of Islamic forces in western Europe. 

Abbasid Caliphate 750-1258 AD (CE) Centered in Baghdad, Iraq, the caliphs of this dynasty were descended from Muhammad's uncle and assumed power after defeating the last Umayyad caliph at the Great River Zab in 750 AD (CE).