This parsha begins the book of Devarim, the fifth, and final, book of the Torah. Another name for the book of Devarim is "Mishna Torah", which means, "review of the Torah" because it contains such a review. However, even though it's a review, more than 70 new mitzvahs are taught here.
At this point, in the first aliyah, the Jews are at the end of 40 years in the desert, and are situated just across the Jordan River from Israel. They have just conquered the Midianite nation, and Moshe Rabeinu's passing away is imminent. In this situation, Moshe Rabeinu begins a rebuke of the people for their misdeeds of the past 40 years. Rashi says that Moshe learned to rebuke just before passing away from Yakov avinu, who rebuked his sons right before his death. This aliyah begins the rebuke.
The second aliyah continues with Moshe's review and rebuke. Here Moshe recounts his appointing a hierarchy of judges (judges over thousands, over hundreds, etc.), then the fact that they were poised ready to enter the land. (In Parsha Yisro, Yisro, who was Moshe's father-in-law, told Moshe the idea of the hierarchy of judges, and also there, Moshe invited Yisro to go to Israel with them because they were only three days away from entering the land.)
In the third aliyah Moshe recounts the episode of the spies, where the Jews sent spies to check out the land of Israel, and all but two of them brought back an evil report saying that the land is unconquerable. The Jewish people believed the spies, and didn't believe that, with G-d, they would have no trouble.
In the fourth aliyah Moshe continues to recount the episode of the spies, including the Jewish people's believing the spies' bad report about Israel. Here it says that the children, as opposed to the adults, will eventually inherit the land, and that G-d told the Jews to turn away from Israel, back to the desert, and wander 40 years. Then some Jews realized their mistake, and proceeded to advance toward Israel anyway, but were immediately attacked by the Emorites because G-d was no longer with them.
In the fifth aliyah Moshe recounts the Jews' travel through certain sections of the desert. These include the land of Seir, which was the land of Yakov avinu's brother Esav's descendants, and the land of Moav, which was the land of Lot's descendants. In each case G-d told the Jews to not fight the people, because the land they are on is theirs to keep as an inheritance. This aliyah ends by recounting the beginnings of the war with Sichon.
The sixth aliyah recounts the war the Jews had with Sichon. G-d made them win easily and the Jews possessed the land of Sichon. Similarly, G-d makes them win over the Bashannites even though their cities had strong, high walls, and bars. This is the land given to the tribes of Reuvain and Gad and half of the tribe of Manasseh on the opposite side of the Jordan from Israel.
The seventh aliyah repeats the instructions to the tribes remaining on the other side of the Jordan. They have to go across the Jordan and fight for Israel with the other tribes, and only after the whole land of Israel is conquered and occupied can these tribes return to their families and their inheritance on the other side of the Jordan. Yehoshua, who will lead the Jews into Israel, is told: Notice how G-d delivered the kingdoms of Sichon and Bashan into the hands of the Jews. Similarly, G-d will do the same thing to all the kingdoms that the Jews will come across when they enter and occupy Israel.