This is parsha Nasso in the book of Bamidbar. Parsha Nasso is the longest parsha in the Torah. It is has 176 pessukim. It is interesting to note that the longest chapter of Tehillim, which is chapter 119, also has 176 pessukim. Furthermore, the longest section of Gomorrah is Baba Basra, and it has 176 pages.
We are continuing now from parsha Bamidbar that ended with the duties of the family of Kehos in the tribe of Levi in carrying the most holy articles of the Mishkan (the tabernacle) whenever it traveled in the desert.
The first aliyah begins with the description of the duties of the family of Gershon. First G-d instructs Moshe to count the members of the Gershon family between 30 and 50 years old. Then G-d gives their service, which is to carry all the tapestries, and the veil and coverings of the Mishkan whenever the Jewish people journeyed.
Then a similar counting is done of the Merori family and their duties are described: they carry the structural members of the Mishkan, such as the beams, boards, pillars, etc.
In the previous aliyah of this parsha, G-d commanded Moshe to count the family of Gershon and the family of Merori. This, the second aliyah gives the total of those counts. The family of Gershon is numbered at 2,630 and the family of Merori is numbered at 3,200. Then the Torah states that Moshe and Aharon and the princes of Israel counted all Levites from 30 to 50 years, which totaled 8,580.
According to Rashi, this third aliyah took place on the day the Mishkan was erected. This is because G-d's presence was now manifest in the Mishkan and so G-d gave rules (mitzvahs) to guard the Mishkan's sanctity.
In this aliyah G-d tells Moshe to instruct the Jewish people that whenever someone becomes tamei (ritually impure), they are to be sent out of the camp. Rashi tells us that there were three camps: first, the Mishkan itself, second, the camp of the Levites around the Mishkan, and third, the camp of the whole Jewish people (Machne Israel).
The three types of impurity referred to here are: tzoraas, the spiritual disease of the skin; the zav, one with a male discharge; and finally, one who is tamei mais, who is tamei from touching a dead body. Someone who is tamei mais is barred from the first camp, the Mishkan. Someone who is a zav is barred from both the Mishkan and the camp of the Levites. And someone who has tzoraas is sent out of all three camps.
The third aliyah then mentions how one who sins against his fellow man must restore the principal plus one-fifth.
This fourth aliyah contains three concepts: the Sotah ceremony in the case of the suspected adulteress, the nazir who dedicates him or herself to G-d, and the priestly blessing. The Midrash Rabba, a book of commentary, dedicates two whole volumes to just this parsha Nasso.
The Sotah ceremony concerns a woman who is suspected of adultery. The woman is brought to the priest with a certain sacrifice. The priest then uncovers the woman's hair and says a prescribed warning, in the form of a curse, to her. The warning/curse says that harm will come to her if she committed adultery, and won't come to her if she didn't. The priest then writes the curse on parchment and dissolves the ink in water, and then the woman drinks the water. If she committed adultery her belly explodes, if not, she is cleared of any suspicion. Not only is she cleared of any suspicion, but blessing comes to her: if she previously didn't have children now she will have children, if she previously had only daughters, now she will have also sons, in all cases improving her offspring.
We can learn many things from the Sotah ceremony, but one is that the ceremony includes the dissolving of G-d's Name (contained in the curse) in the water that the suspected adulteress drinks. Normally, it is forbidden to erase G-d's Name, but in this case we see that G-d is willing to have His Name dissolved in order to clear up any suspicions that a husband may have for his wife. We therefore learn how we should bend over backwards for the sake of peace between a husband and wife.
Next, in this aliyah, we have the law of the Nazarene who vows to abstain from wine and other grape products for a certain period of time, and at the end he/she brings offerings including a sin offering. This shows that although it's a holy thing to become a Nazir, to abstain from the kosher physical pleasures that G-d gives us (like wine) is somewhat of a sin.
Finally this aliyah contains the priestly blessing, which are recited by Kohanim in the synagogue on Yom Tovim. (The holiday instructions for the priestly blessing service are given on page 268 of the siddur "Tehillat Hashem".)
The fifth aliyah begins the descriptions of what the princes of the tribes offered when the Mishkan was set up. This section of Torah is the same Torah reading that is used during the eight days of Chanukah, and is read by us after davening during the first twelve days of the month of Nissan.
The sixth aliyah continues the descriptions of what the princes of the tribes offered when the Mishkan was set up.
The seventh aliyah completes the descriptions of the princes' offerings when the Mishkan was set up. It also completes the description of the dedication of the Mishkan and describes how Moshe spoke with G-d in the Mishkan.