The Law of God is a set of rules, commands, and instructions which God revealed to Moses. God gave the law, whereas Moses was the one who documented it and communicated it to the Israelites. As such, the Law of God is sometimes referred to as the Law of Moses.
The Law of God is recorded in the books of Leviticus and Deuteronomy, forming the basis of belief for the Jewish people.
Jesus, however, came to fulfill this law (Matthew 5:17).
In the Bible, Law is used narrowly to refer to the Ten Commandments and more broadly to represent the entire body of commands and instructions given to Moses by God for the Israelites to follow.
Some people (such as the Hebrews in the Old Testament) follow the Law with a legalistic fervor, with their relationship to God becoming a list of dos and don’ts. This wasn’t what God intended or wanted from them.
Jesus said he came, not to replace the law but to fulfill it (Matthew 5:17). This signaled an change of perspective away from the letter of the law to the intent behind it.
Also, see Law of Moses / Law of God.