In the first aliyah Moshe addresses the people saying that he is 120 years old today, and he is not permitted to go over the Jordan with them. Yehoshua will lead them, and G-d will go with them and fight their enemies for them
The second aliyah elaborates further that G-d will do to the inhabitants of the land as He fought Sichon and Og, kings of the Amorites. G-d destroyed them and gave their land to the Jews. We should be strong and not fear, G-d will not forsake us.
In the third aliyah Moshe calls Yehoshua and tells him to be strong and with courage, and that he will cause the Jewish people to inherit the land of Israel. The Torah says here that Moshe writes the Torah at this point and gives it the Leviim and the elders to keep and teach the Jews.
In the fourth aliyah Moshe gives the commandment of Hakhel (meaning assemble), where every seven years all the men, women, and children are to assemble at the time of the festival of Succos, and hear the Torah read, so that they will learn the Torah and obey, and fear G-d. In years following Shmittah years, the Lubavitcher Rebbe has called for Hakhel years with many gatherings during the year.
In the fifth aliyah we return to some narrative of action in the story of the Jews in the desert, rather than Moshe's review of the Torah that we've had since the beginning of the book of Devarim. Here, G-d says to Moshe that the day of his passing away is approaching, and that Moshe should come with Yehoshua to the Mishkan. They go there and G-d appears to them and tells Moshe that after he passes away, the Jewish people will abandon G-d and stray after the alien gods of the land and evil troubles will befall them. Therefore G-d tells them to write the song contained in the next parsha (Ha-azinu) as witness of why the troubles befell them. The Talmud (Sanhedrin 21b), derives the halacha for every Jew to write a Torah from this passage. The Rebbe instituted a very easy way to participate in this mitzvah, and at the same time unite Jews, and that is by every man, woman, and child buying a letter in a sefer Torah.
In the sixth aliyah Moshe writes down the song and teaches it to the Jews. Moshe encourages Yehoshua to be strong and brave.
The Torah then says that Moshe finished writing the Torah to the very end.
In the seventh aliyah Moshe gives orders that the Torah he wrote should be placed by the side of the ark of the luchos (tablets) as a witness.
Moshe believes that the Jews have been rebellious in his life, so surely they will be so after his death. (In actual fact, however, the Tanach later states that the Jewish people remained righteous during the entire lifetime of Yehoshua, Moshe's student, in the merit of Moshe.)
Moshe speaks the words of the song into the ears of the entire Jewish people.