Even on days when we do not usually read Torah at morning services, if it is Rosh Hodesh, the beginning of the new month (on the Jewish calendar), we read Bamidbar (Numbers) 28:1-15.
Let’s start from the beginning. We read Torah in the morning on Monday, Thursday, and Saturday, all from the same parashah (portion) designated for that week. (If you want a head start on the Shabbat Torah reading, come to morning minyan!) However, if it is Rosh Hodesh, even if it’s not Monday or Thursday, we read the special Rosh Hodesh parashah. And while the weekday readings are broken into three aliyot, and the Shabbat readings are broken into seven plus a maftir to lead into the haftarah, the one for Rosh Hodesh is broken into four aliyot.
Why four? Well, the rules are complicated, and there are a bunch of them. Essentially each aliyah must contain at least three p’sukim, three verses. And we must not start or stop within three p’sukim of a paragraph break, lest someone walking in mistakenly assume we had read two p’sukim for an aliyah. Thus we split it up into four parts, and repeat one of the p’sukim: lines 1-3, 3-5, 6-10, and 11-14. (There are others who split the parashah differently, for instance 1-3, 4-8, 6-10, and 11-14, which repeats 6-8.)
When Rosh Hodesh occurs on Shabbat, we read the usual weekly parashah, and add Numbers 28:9-15 as the maftir. On Rosh Hodesh Tevet, though, during Hanukkah, we read verses 28:1-15, in three sections, and then add - from a second Sefer Torah - the Hanukkah reading for that numbered day.
Not only that, gentle readers, but we have four aliyot also for Hol HaMo’ed Sukkot (different for each day), and also for Hol HaMo’ed Pesah. On Hanukah - and wait until you hear this! - we read three aliyot (or some break it into four) on the first day, beginning with Numbers 7:1, and then on each successive day we read the two aliyot designated and then add the whole next day’s reading.
It goes in order of importance: Rosh Hodesh and Hol HaMo’ed are considered half-holidays, so they get one extra aliyah beyond the three (total of four), and the hierarchy proceeds from there. On Rosh Hashanah, Sukkot, Pesah, Shavu’ot, Sukkot, Shemini Atzeret, and Simhat Torah, we have five aliyot. And on Yom Kippur morning we have six. (When Yom Kippur or a festival occurs on Shabbat, we have seven.)
Moreover, there are times when rabbis have added aliyot for special occasions. What if a congregation has so many simhahs that there are not enough aliyot to cover them? The answer might just be to add one or two.