The seventh aliyah gives the law of an individual committing an act of idolatry inadvertently, and also if he does it, G-d forbid, on purpose. Then an incident is described where a man is found gathering sticks on Shabbos. Rashi says that this happened on the second Shabbos after the giving of the Torah. Therefore the Jewish people properly observed only one Shabbos until today. It says in the Talmud that if the Jewish people observed even two Shabbos's properly (which means just one more), we would immediately be redeemed and Moshiach would come, may it happen speedily in our days.
The last part of this aliyah contains the commandment of putting tzitzis on our four-cornered garments. This part of the aliyah is what we say for the third paragraph of the Shma Yisroel. On the subject of tzitzis, the Torah tells us that if we look at them, we will remember all of the commandments. On this, Rashi says that the gematria of the word tzitzis is 600, add that to the  threads, and the 5 knots and they total 613, the number of commandments.