I will only discuss two important and major laws here, though of course there are many more.

The International Statute of Wizarding Secrecy- The International Statute of Wizarding Secrecy, also referred to as the International Code of Wizarding Secrecy and commonly shortened to International Statute of Secrecy or ISoS, was a law in the wizarding world that was first signed in 1689, then established officially in 1692. The law was laid down by the International Confederation of Wizards to safeguard the wizarding community from Muggles and hide its presence from the world at large and is now upheld by the Ministry of Magic.

The Decree for the Reasonable Restriction of Underage Sorcery- The Decree for the Reasonable Restriction of Underage Sorcery is a bylaw of the Ministry of Magic, which was written in 1875, and which bans the use of underage magic outside of school. The Decree is enforced by the 'Improper Use of Magic' Office in the Ministry of Magic. The restriction is for wizards and witches who are under the age of seventeen, upon whom The Trace still operates. Even so, the Ministry recognizes that they may have to use magic in certain situations such as self-defense in a life-threatening situation. In addition, young children of below school age, or children who are not in possession of a wand, are mostly exempt from the rule since they usually have little or no control over the magic they accidentally perform. Overall, it appears the Ministry of Magic generally limits enforcement of the decree to situations where underage wizards or witches perform magic in front of Muggles. Paragraph C of the clause states that it is a crime to knowingly perform magic in a Muggle-inhabited area and in the presence of a Muggle. However, Clause 7 also states that magic can be used in front of Muggles in exceptional circumstances, including situations when the life of the witch or wizard is threatened, or the lives of other witches, wizards and Muggles are threatened. Also, it seems that a high-authority person may give permission for an underage student to perform magic under certain circumstances, as late former Hogwarts Headmaster, Albus Dumbledore gave Harry Potter such an instruction if an attack was to eventuate, when he was 16 years old.