In this chapter, Moses begins recounting the history of Israel, beginning with their departure from Mount Sinai.
It's exciting to be starting a new book. I'm excited; are you excited? You should be, I mean think of all the laws we're going to get to read about. The best part is that this entire book is 100% Moses talking. The entire book is just one speech after another. I should really stop before I scare off my entire audience (which is not very large to begin with).
Starting in verse 1, we can see that this book is set right at the conclusion of Numbers, with Moses and the Israelites camping "across the Jordan", to the east. We can also see that it is the fortieth year, right at the end of their 40 years of wandering in the desert.
Starting in verse 6, Moses begins his oration by reminding us of their journey from Horeb to the promised land. Horeb is the same place as Mount Sinai, and the terms are used interchangeably (for instance, Horeb was used in Ex 3:1, Ex 17:6, Ex 33:6). It's interesting that he begins at Horeb/Sinai, because that is where the covenant between God and Israel was first formed. This oration, then, is a brief history of Israel since entering the covenant.
This is also part of the standard Hittite suzerain treaty I mentioned in my introduction to Deuteronomy. Generally these treaties would begin with an account of the history between the lord and the vassal, providing an explanation or background for why the vassal is in debt to its lord and expounding on the general virtue, greatness, majesty, etc. of the lord.
In Deuteronomy, it has the dual purpose of establishing the sins of the Israelites and the generous mercy of the LORD. This, in addition to the LORD's continuing protection of Israel, is the basis of the LORD's claim on their allegiance.
Overall, the story here is greatly abbreviated when you compare it to Exodus. There are only a handful of episodes included here, such as the appointment of leaders (v. 9-15 here, cf. Ex 18), and most significantly the refusal of the people to enter the promised land, from Num 13-14.
This chapter contains a bit of a reversal compared to the story in Num 13. In Num 13:2, the LORD commands Moses to send the 12 spies. In v. 22, Moses says that the Israelites proposed to him to send the spies. I think this is meant to go along with the polemical style I talked about in my introduction. Moses is trying to assign full responsibility to the people, so that they would not try to blame the LORD for what resulted. Note how lovingly the LORD is depicted here, carrying the Israelites through the wilderness "just as a man carries his son". This loving concern heightens the sense of Israelite treachery when they refuse to trust the LORD and take the land to which he was leading them.
Overall, while this chapter leaves out a lot of the story from Exodus and Numbers, what it does include largely agrees with what we had read there. The language is very different, but there are not really any big discrepancies and this chapter doesn't really add anything to the Exodus/Numbers account.