The varying levels of reverence and precedential importance accorded to Muhammad, his family, his companions, their contemporaries, and each successive generations is of great importance in the Islamic tradition. The reasoning for this importance is best understood in light of the fact that the Islamic tradition is one centered on the precedence set by individual persons, rather than on the particular arguments for or consequences of any given practice or belief. This is not to say that thinkers in the Islamic tradition did not elaborate and discuss the reasons for and consequences of any given practice or belief (be it religious or legal), but that, at the end of the day, these considerations were always secondary and tertiary to the authority of the individual who first implemented them. As a result, the variety of persons responsible for instituting a practice is overwhelmingly the justification for it, although other considerations may be factored in subsequently. More important than these other considerations, however, will always be the interpretations of the given practice or belief advanced (usually by subsequent generations or groups of persons of lesser authority, although a party may in some cases explain its own reasoning). Broadly speaking, therefore, the first question is in all cases is
who said to believe or do this? ('Muhammad' being the best possible answer), the second question is
who interpreted this practice or belief? (here again, as always, Muhammad is the best answer, however one will almost always need to look to Muhammad's companions or successors for an explanation), and the third question is
what can be said rationally about this practice? (by this point, however, the room for autonomy on the part of the jurist or theologian is usually considerably diminished if not altogether gone). At each level, one hopes for the highest authority available, but available references usually increase in descending order and one will not, of course, expect to find an explanation for the actions of Muhammad's successors from someone who preceded them, such as, say, Muhammad himself.
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The Sahabah were the companions of Prophet Muhammad. According to tradition, an individual must have: seen Muhammad, believed in his prophethood, and died as a believer in order to be considered a sahabi or companion of the Muhammad (and thereby attain the concomitant theological status). These would exclude, for example, Ubayd-Allah b. Jahsh (brother of Zainab b. Jash, the cousin and wife of Muhammad), who was considered one of the sahabah but later converted to Christianity.
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The Ahl al-Bayt, literally "People of the House", is a term used to refer to those persons who are members or descendants of Muhammad's household. These people have a priveleged status in Islamic and especially Shi'ite doctrine. A sahih hadith reports Muhammad to have said, "I have left among you, that which if you hold fast to it, you shall not go astray: The Book of Allah and my family". Traditions of this sort have been variously interpreted by the many sects of Islam.
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The Rashidun Caliphs are the four caliphs who followed in the leadership of the ummah following the death of the prophet Muhammad, Abu Bakr, Umar, Uthman, and Ali. Sunni jurists consider them "rightly guided by Allah" and see their reign and religious ordinances as a basis for the practice of Islam. Shi'ites, however, consider the first three to be usurpers, with only Ali and his family having the right to sit on the throne.
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The Tābi‘ūn (التابعون Followers) are the generation of Muslims who were born after the death of Prophet Muhammad, but who were contemporaries of the Sahabah (Companions of Muhammad). As such, they played an important part in the development of Islamic thought and philosophy, and in the political development of the early Caliphate. According to Muhammad, they are among the best generation of Muslims on Earth, along with the Tabi' al-Tabi'in and the Sahabah.
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Salaf is an Arabic noun which translates to "predecessor", or "forefather". In Islam it refers to the first three generations of Muslims, the so-called "Pious Predecessors". According to Prophet Muhammad in the hadith, the Sahabah ("Companions"), Tabi'un ("Followers"), and Tabi' al-Tabi'un ("Those after the Followers") are among the best generation of Muslims on Earth, and are therefore considered the model for how Islam should be practiced.
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Alongside Muhammad himself, who consummated his marriage to nine year old Aisha when he was 54, his companions also committed engaged in child marriage. The most famous example of this is, perhaps, the marriage of Umar b. al-Khattab to Umm Kulthum (the daughter of Ali b. Abi Talib when he was 58 years of age and she was between 10-12 (some sources suggest she was even younger).