Identify the category of law that would apply in this situation:
you are walking past your neighbours yard when their pit bull breaks through the unlocked gate and sinks its fangs into your leg. You sue for damages.
The broad category of law that would apply in this situation would be civil law. The person who owns the dog has not committed any crime and therefore this case would not involve criminal law.
More specifically, this would be an issue in which you would allege that a tort has occurred. A tort is a claim that a civil wrong has been done to you and that a specific person (in this case the owner of the dog) should be held liable.
Within tort law, this would be an issue of negligence, not an intentional tort. Negligence occurs when someone's conduct falls below the standards that the law sets in terms of their duty to protect other people. You will need to claim that the dog's owner failed to protect you adequately by having the dog more effectively restrained (by locking the gate or chaining the dog or having a stronger gate, for example).
Most, if not all states have specific dog bite laws, in my state, Ohio, it is STRICT liability, meaning no fault/negligence has to be shown to prevail.
I have read case law on my state before, unless the dog was so called tormented/teased, the liability is Strict. One case I remember was a 2 or 3 year old is not capable of such, if the owner/caretaker argues that as a defense to refute SL.
Depending on the facts, there may be a criminal law that has been violated.