Short answers, pulled from the story.
In the terminology of law, assault is the act of causing physical harm or unwanted physical contact to another person, or in some legal definitions the threat or attempt to do so. It is both a crime and a tort, so it may result in criminal prosecution, civil liability, or both.
Battery refers to the actual bodily contact, the deliberate use of physical force against another person, while assault traditionally refers to a credible threat or attempt to cause battery. Some jurisdictions combined the two into a single crime called "assault and battery", later shortened to just "assault", and civil law and Scots law have never distinguished the two.
Aggravated assault is a stronger form of assault, usually involving a deadly weapon, and is typically classified as a felony. A person commits it by attempting to cause serious bodily injury with a deadly weapon, having sexual relations with someone under the age of consent, or causing bodily harm by recklessly operating a motor vehicle during road rage.
Consent may be a complete or partial defense to assault, but in England it is not a defense where the injury is severe unless there is a legally recognized good reason such as surgery, contact sports, bodily adornment, or horseplay. In Scottish law, consent is not a defense for assault at all.
Assault in Ancient Greece was normally termed hubris, which referred to actions that intentionally or unintentionally shamed and humiliated the victim and often the perpetrator. It was considered the greatest sin of the ancient Greek world, and two well-known cases appear in the speeches of Demosthenes, Against Meidias and Against Konon.
In the United States, assault can be charged as either a misdemeanor or a felony and is often subdivided into simple assault and aggravated assault. Laws vary by state, so acts classified as assault in one state may be classified as battery, menacing, intimidation, or reckless endangerment in another.