This is the post #27 of the Calvin's Institutes summary series.
This chapter is about the Ten Commandments. Calvin expounds each of them, and here are some interesting or helpful points I've found.
Calvin takes that the Ten Commandments are still in force for Christians, although he seems to take the Sabbath law (the 4th commandment) with a caveat. He thinks the first commandment, by which he means to take the verse 2 as well as verse 3, is something of a preface to the whole law. This does not mean that it is not a commandment, but rather it is the whole sum of the law, which also introduces who God is and what He has done already for His people.
On the 3rd commandment, "You shall not take the name of Jehovah your God in vain": Calvin is against taking God's Word in vain too since it dishonours God. Also, even though some take such a view based on the Sermon on the Mount, Calvin believes and explains how taking oaths are not always wrong (see section 26–7).
On the Sabbath Day (the 4th commandment): Calvin is not as Sabbatarian as the Westminster Confession of Faith states. Calvin teases out three purposes for this law: 1) Causing Israelites to look forward to the spiritual rest, 2) taking a regular time for public and private worship of God, 3) giving a day of rest to people from their work. That first purpose is abrogated now that Christ has come, but the other two are still in effect. However, it is wrong to strictly insist on a certain way of observing the Sabbath day or the Lord's Day (Sunday) because that is superstitious. The Lord's Day is not a simple continuation of the Sabbath Day for Christians. We should use the Lord's Day to meditate on the eternal rest, and engage with God's Word in public and private worship, and give rest to anyone under our authority.
Calvin strongly argues against the opinion that "Do not take vengeance; love your enemies" is not a commandment but a counsel (advice, wisdom).
Calvin also argues against the notion that there is a distinction between mortal sins and venial sins. He argues that all sins are mortal in that it incurs God's righteous judgment, that is, death.
"Let the children of God hold that all sin is mortal. For it is rebellion against the will of God, which of necessity provokes God's wrath, and it is a violation of the law, upon which God's judgment is pronounced without exception. The sins of the saints are pardonable, not because of their nature as saints, but because they obtain pardon from God's mercy." (Calvin, Institutes, II. viii. section 59.)
(There are many other great insights, which I quoted in separate posts.)