An ordinance tracing back to Moshe mandates that Jews read from holy Torah scrolls written in ink on parchment every Shabbat, Monday, and Thursday (BK 82a). Due to the holiness and exaltedness of Shabbat, the Sages instituted that seven people should be called up to read from it, corresponding to the seven days of the week (Megilla 21a). In talmudic times, it took communities in Eretz Yisrael three years to cycle through the entire Torah, while in Babylonia it was completed annually. The current custom throughout the Jewish world is to complete the Torah each year on Simĥat Torah. This is done by reading the weekly parsha each Shabbat. Each of the seven people called up to the Torah reads part of the parsha (referred to as an aliya); together they complete the entire parsha. If one Shabbat a congregation is unable to read the parsha, the next week it must read two parshiyot and make up for the one missed (Rema 135:2).
If a congregation wishes to call up more than seven people to read, they may do so as long as each person reads a minimum of three verses. Some maintain that nowadays one should not add to the seven because that involves reciting additional berakhot – more than were instituted by the Sages. It used to be that the first person called up would recite a berakha before reading and the last person called up would recite a berakha after reading, but all the people called up in the middle would not recite berakhot. Later on it was instituted that everyone called up should recite a berakha before and after their aliya. This was due to concern that people who arrived or left in the middle of the Torah reading would not realize that a berakha was recited at the beginning and end of the parsha. Accordingly, nowadays each person who is called up recites two berakhot. Thus it is improper to add additional aliyot, which would involve the recitation of even more berakhot, beyond those instituted by the Sages. Furthermore, it is also important not to burden the congregation by extending the prayer service. Therefore, ideally a congregation should not add to the seven aliyot. However, in a time of need and to avoid offending someone deeply, one may do so (SA 282:1-2; MB ad loc. 4-5).
Technically, an aliya may be given to a minor who is old enough to know to Whom berakhot are addressed. This is on condition that the majority of the seven people called up are adults. There are Sephardim who follow this position (SA 282:2; Yeĥaveh Da’at 4:23). The Ashkenazic custom, and that of some Sephardim as well, is not to call up a minor to the Torah. There are some Sephardim who follow the position of Arizal and call up a minor for the seventh aliya but for no others (see MB 282:12; Kaf Ha-ĥayim ad loc. 22). The Yemenite custom is to call up a minor for the sixth aliya.