Shevuos, chapter 3, mishnah 8. This mishnah comes to define what a shevuas shav (a vain oath) is, and to list its categories: "Eizohi shevuas shav?" - Which oath is a shevuas shav?
The first category - "nishba leshanos es hayadua la'adam": one who swears to contradict what is known to people.
This refers to an oath that describes something differently from the reality known to people. The Gemara explains that it must be a matter known to at least three people. These are the mishnah's examples:
"Amar al ha'amud shel even shehu shel zahav" - a pillar made of stone, and the one taking the oath claims that it is made of gold, when this is not the reality and at least three people know it.
"Al ish shehu ishah" - one who swears about a man that he is a woman.
"Al ishah shehu ish" - one who swears about a woman that she is a man.
The second category - "nishba al davar she'i efshar": one who swears about something impossible.
A person who takes an oath about something that cannot possibly be. These are the mishnah's formulations:
"Im lo ra'isi gamal shepore'ach ba'avir" - a flying camel.
"Im lo ra'isi nachash k'koras beis habad" - a snake shaped like the beam used in an olive press, and no such thing exists in reality.
And what exactly is the case here? A person who forbids all the fruits of the world to himself by an oath, and makes it conditional: "All the fruits of the world are forbidden to me if I did not see a camel flying in the air." In other words, he wants to stress that he really did see it, since otherwise all those things become forbidden to him. The mishnah explains: since it was in his power to forbid all the fruits of the world to himself without any condition at all, it is clear that the purpose of the oath is to state something impossible; and the very act of swearing about something impossible is a shevuas shav.
The third category - an oath to nullify a mitzvah:
"Amar la'edim: bo'u vaha'iduni" - one who says to witnesses who possess testimony that would help him that they should come and testify on his behalf, as the Torah obligates them to do. And they respond: "Shevuah shelo na'id" - they swear not to testify, contrary to the Torah's command. The same applies to one who swears not to perform a particular mitzvah:
"shelo la'asos sukkah" - not to make a sukkah.
"veshelo litol lulav" - and not to take a lulav.
"veshelo lehani'ach tefillin" - and not to put on tefillin.
"Zo hi shevuas shav" - this is a vain oath. And the rule of a vain oath is: one is liable to lashes for a deliberate violation, and exempt for an inadvertent one. One who swears a vain oath deliberately receives lashes, while one who does so inadvertently is exempt, and is not required to bring any offering or any form of atonement.
An additional category in the words of the Rambam:
The Rambam cites, in the name of the Yerushalmi, a further category of a false oath, one that is perhaps more familiar to us: someone who swears about a matter that is already known to be true, such as one who says about a stone that it is a stone. This is an oath with no purpose, an oath that carries no practical consequence and no meaning, since everyone already knows that this is the truth. There is no reason whatsoever to swear about something that no one doubts, and therefore this is a false oath.
In summary: In this Mishnah we learned three categories of a false oath - one who swears to contradict what is known to people, one who swears about something impossible, and one who swears to nullify a mitzvah or to refrain from giving testimony; the law of a false oath: lashes for an intentional violation and exemption for an unintentional one; and the additional category brought by the Rambam in the name of the Yerushalmi - one who swears about a matter known to be true.