This parsha begins the fourth book of the Torah, named Bamidbar. Last week we completed the reading of the sefer Vayikra, which started just after the Mishkan was completed on the first of the month of Nissan, one year after the Jewish people left Egypt. This book of the Torah, and this parsha, begin one month (30 days) later, on the first of the month of Iyar of that same year.
In the first aliyah, G-d commands Moshe to count the Jewish people another time. Rashi says that G-d counts the Jews because they are precious to Him. The first counting was when the Jews first left Egypt, the second was after some were lost after the sin of the Golden Calf to see how many remained, and this time they are counted again since now the Divine Presence abides with them in the Mishkan.
In the second aliyah, the Torah gives the number of people counted in each tribe. Note, however, that G-d told Moshe not to count the Levites. The total number of Jews counted was a little more than 600,000 not counting the Levites. (Rashi says that a reason for not counting the Levites was that those people counted were destined to eventually die in the desert, but the Levites weren't to be included since they didn't take part in the sin of the chet ha-egel--the sin of the golden calf.) Here the Levites are given charge of dismantling, carrying, and erecting the Mishkan whenever it was to move, and they were to camp near it while all the other tribes camp in their own camps.
In the third aliyah G-d commands the manner in which the Jewish tribes are to camp around the Mishkan, each with a flag of a unique color which Rashi says was the same color as that tribe's stone on the breastplate (Choshen Mishpat) of the Kohane Gadol. Rashi also says that the way the tribes camped in the desert is the way Yakov Avinu's sons carried their father Yakov out of Egypt to his burial in the cave of Machpella, and as we know, the tribes descended from Yakov's sons.
This aliyah also gives the order of the departing of each tribe whenever the Jewish people journeyed in the desert.
As we've learned previously in the Torah, the Jewish people would know to journey when the cloud of G-d's glory moved. Until this time the cloud rested on the Mishkan.
The fourth aliyah begins with the words "these are the generations of Aharon and Moshe" and then goes on to discuss only the sons of Aharon. Rashi says that they are called the sons of Moshe because he taught them Torah.
Here, the tribe of Levi is appointed to take care of the Mishkan. Rashi says that since the Levites are doing this service as agents of all the Jewish people, the Jewish people give their tithe to the Levites. The Torah mentions that this honor originally belonged to all the first-borns, and Rashi says that because they participated in the chet ha-egel (sin of the golden calf) the first-borns lost the honor.
In the fifth aliyah G-d commands Moshe to count the Levites. The criterion for counting the Levites is that they should be males from a month old upward. One of the verses in this aliyah says: "Moshe numbered them according to the word of G-d." Rashi says on that verse, that Moshe asked G-d how he could possibly go into tents to count the babies (who were included in the count starting at one month old), and G-d said "you do your part, and I'll do Mine"; Moshe went and stood outside each tent and a Divine voice came from the tent saying that such and such a number of infants are in this tent.
In the sixth aliyah G-d tells Moshe to take a census of the names of first-born Israelites, and again the criteria for counting them is that they be one month old or older. This census resulted in approximately 22,000. G-d then tells Moshe to take the Levites instead of the first-born to be G-d's.
The seventh aliyah is about the special duties of the Kehos family. After Aharon and his sons initially cover the most holy items of the sanctuary, the Kehos family are to further cover the items and, when the whole camp journeys, the Kehos family would actually carry these items. The holy items that they were thus responsible for included the Aron HaKodesh containing the luchos (the tablets with the Ten Commandments on them), the Menorah, the Golden alter, etc. The Kehos family are to start their work only after Aharon and his sons do the initial covering, so they (the Kehos family) would not die from touching these most holy things.