The mitzvah to learn Torah is a basic commandment, on which all the other mitzvot depend. There is no specific time for Torah study; instead, it is a mitzvah to learn Torah at all times, as it is written (Joshua 1:8), “You shall meditate upon it day and night.” In order to strengthen Israel’s connection to Torah, Moshe Rabbeinu instituted the Torah reading on Shabbat, and in Shacharit of Yom Sheni (Monday) and Yom Hameshee (Thursday), so that three days will not pass without hearing Torah (Rambam Tefillah 12:1).
The Chachamim teach (Bava Kama 82a) that this was instituted based on the verse (Exodus 15:22), “They traveled for three days in the desert without finding any water.” Moshe Rabbeinu, and his disciples, the elders and the prophets, understood that the thirst for water was a result of three consecutive days during which Israel did not communally engage in Torah study. Torah is likened to water, for just as water sustains all that lives and grows in the world, so Torah sustains the soul. Since the nation became slightly detached from the Torah, the springs of water also ceased to flow. Although the Torah scholars of that generation most probably learned Torah during those three days, for three days the nation of Israel did not engage in Torah publicly. Therefore it was established that the Torah would be read every Monday, Thursday, and Shabbat, so that never again will more than three days pass when Israel does not publically read from the Torah.
Ezra HaSofer further instituted that, for the Torah reading on Mondays and Thursdays, three people are called up to the Torah. Each person called up reads at least three verses. All together ten verses must be read (Bava Kama 82a; Shulchan Aruch 137:1-2; additionally, in Peninei Halachah Likutim, part 1, 4:2-3, the reasons for this halachah are explained).