We cannot have a class on Occlumency without talking about Legilimency as well. If Occlumency is the act of protecting one's mind, Legilimency is the act of magically navigating through person's mind in order to reveal their thoughts, feelings and memories, as well as correctly interpreting them. A witch or wizard that uses this particular branch of magic is called a Legilimens. Legilimency is not completely unknown to Muggles, as opposed to Occlumency. They call it mind-reading, though magic folk are not fans of the term, as they deem Legilimency subtler and more refined. Interestingly, Legilimency is not unique to humans, with some beasts and objects capable of it in its rudimentary form, like Wampus cats and The Sorting Hat.
Legilimens is the incantation of the spell. Etymology of it is pretty straightforward. It is a compound of the Latin legere, meaning 'to read' and mens, meaning 'mind'. The spell itself can be performed in many ways, with a wand and incantation said aloud, or nonverbally, as well as wandlessly, though the latter is significantly harder to do. When a target is not adept at Occlumency, upon invading their mind, Legilimens will be able to detect if they are lying, as well as access their thoughts, emotions and memories, bringing them to the forth of the target's mind. Some highly skilled Legilimens can also plant false memories and visions inside a person's mind or to temporarily possess their body. While eye contact makes it easier to perform Legilimency, it is not necessary.
The history of Legilimency is a mysterious one, since no one really knows how the art had started, or who invented it. The earliest report of a Legilimens is Salazar Slytherin, who lived in 11th century. Another skilled Legilimens was Severus Snape, who, during the time when Second Wizarding War started, taught Harry Potter the art of Occlumency to protect himself against Lord Voldemort. Snape was able to perform Legilimency nonverbally and wandlessly, only needing eye contact with a person. He used this ability during duels as well, knowing all spells his opponents used, which made him able to counter and negate then before they could be cast.
As mentioned in a previous paragraph, Lord Voldemort was a frequent and able user of Legilimency, which is quite impressive, as Legilimency is one of the toughest branches of magic to master. He used it mostly for interrogation, and unlike other people, he was actually enjoying invading people's minds. He also had a direct link into the mind of Harry Potter, made as a result of a failed Avada Kadavra on the night he killed Potter's parents, which was assumed to have helped with Voldemort's use of Legilimency.
Another accomplished Legilimens was Albus Dumbledore, who rarely employed this tactic, and only when it was of utmost importance. He used it on Kreacher, Black family house-elf, when he needed to find out how was Harry Potter lured to the Department of Mysteries.
Interestingly enough, while Legilimency and its use is governed by the power of the witch or wizard there are some that are just born with the talent. They use it without effort, and sometimes, even without meaning to. One such person is Queenie Goldstein, an American witch who was employed at MACUSA (Magical Congress of United States of America). She was a very talented Legilimens and kept reading the minds around her, such as Newt Scamander and her sister Porpentina Goldstein, responding to them verbally, as if they were in conversation. It seems that she did so accidentally, without real meaning or malicious intent.
Similarly to Occlumency, you will not find Legilimency on a regular Hogwarts curriculum, as it invades most basic of human rights, the right to privacy, especially when it comes to one's mind.