Solid job on a sometimes-controversial subject. Peterson is perhaps the most workmanlike systematician out there today. He isn't fancy, and is rarely profound, but you don't need to be when you're job is to systematize beautiful Scriptural truths.
After the required chapter on the doctrine of election through church history, Peterson looks at every text he can in Scripture that addresses the topic. They basically break down into three categories: corporate (Israel/church), individual (the elect foreknown before the foundation of the world), and messianic (Jesus' election as the anointed one). Again, nothing elaborate, just a good survey of the relevant texts.
It's his last few chapters that really bring home the bacon. Chapter 8 addresses free will--that of Adam and Eve, that of unregenerate sinners, that of the redeemed, and that which we will enjoy in the new heavens/earth. He then asks a seemingly simple question: why are we saved? Peterson points to four answers: because we trust Christ as savior, because we're born again by the Spirit, because Christ died and rose for us, and because the Father elected us. Note that all four are true, but their temporal sequence matches their order of precedence: election is the primary reason, and because we were elected X died for us, and therefore the HS worked in our heart, and therefore we trust X for salvation. Mess this order up, and you mess up the biblical teaching on election.
You can also look at the other side: why are people condemned? They are condemned, in reverse order, because of the sins they commit, because of Adam's original sin, and because they were passed over by God (preterition). Again, the order is vital to understanding how God's election works. He doesn't elect or not elect us based on our faith or lack thereof; it's precisely the opposite. The rest of Chapter 8 demonstrates how both God's sovereignty and man's responsibility are held as valid in Scripture. He then looks at various schemes that fail in understanding the relation between the two: fatalism, hyper-Calvinism, Arminianism.
Chapter 9 is a comprehensive summary of the Biblical story of election, and then Chapter 10 concludes in a remarkable way--Peterson shows how the objections to election are actually areas that election applies to the faith of a believer. Let me explain. For instance, some say election is unfair or arbitrary, but in fact Scripture says it is a reason to praise God. Some say it fosters elitism; Scripture says it should foster thanksgiving and humility. Some say it retards evangelism; Scripture says it incentivizes it (I love Acts 18:9-10). Some say it leads to fatalism; Scripture says it should lead to perseverance and service. Some say it is defeatist; Scripture says it inspires confidence in God. Some say it leads to struggling with assurance; Scripture says it leads to assurance of God's love (just read John 10:27-29). I thought this chapter was a great finish to a well-done book.