Masechet Sanhedrin, Perek Aleph (Chapter One), Mishnah Aleph. There are three different levels of Batei Din, of Jewish courts. The lower court is a small Beit Din with three judges. The next-level court has 23 Dayanim, judges. The high court, the great Sanhedrin of the Jewish people, has 71 judges. That Sanhedrin was in the Lishkat HaGazit, the chamber on Har HaBayit in the Beit HaMikdash. The larger the court, the more people were there, the more power and authority it had, and the more different types of situations it could deal with. This Perek, this chapter, would deal with which cases are judged by which type of court.
The Mishnah says, Dinei Mamonot Bishlosha: any type of case that deals with money. This includes disputes about a loan: if somebody gave another person money, if he let him borrow money from him, and then they bring people to testify that the person did borrow money. All of this is dealt with in a Beit Din of three judges. They could even use judges in this type of case who do not have Semichah. Semichah means that the previous generation, the rabbis of the previous generation, have approved you and given over their tradition. They are relying on you to pass the tradition over to the next generation.
Usually, throughout the Mishnayot, we're going to be talking about Dayanim, judges who have Semichah. But only here, in cases of loans, we're talking about judges who do not have Semichah. They can even be used because we don't want people to think that if they get into a troublesome situation, they're going to have to find rabbis who have Semichah. We will say that even rabbis who don't have Semichah can deal with these types of cases. They're easier to find, and there's less hassle in finding them. So it'll encourage people to do the mitzvah (commandment) of lending people money.
When there are situations involving thievery, theft, or injury—if somebody hurts one of his friends and has to compensate him—these can also be dealt with by a court of three people, three judges. Nezek means damages that are done by animals, and Chatzi Nezek is half damages. If an animal causes damage intentionally, then the owner would only have to pay half Nezek. This is back to Masechet Bava Kama, because an animal is not expected to damage on purpose. So it's not considered to be an expected damage; it's only Chatzi Nezek, half the damage it causes.
And also, Tashlumei Kefel. If somebody steals, a ganav (thief), he has to pay the owner double. He has to pay double whatever he stole, as a penalty for what he did. Also, if a person steals a sheep or a goat and slaughters or sells it, he has to pay the owner four times the value of the animal. If he stole an ox and slaughtered or sold it, he has to pay the owner five times the value of the ox. Three judges are enough for all of these different things. A Beit Din made up of three would be sufficient to deal with these cases.
If there's a situation involving an ones, a violator—a man who forces a woman to be with him—or a mefateh, a seducer, someone who convinces a woman to be together with him—or, thirdly, a man who gets married to a woman and spreads terrible rumors about her, saying that she went with another man between the kiddushin (halakhic engagement) and the nisuin (wedding)—all of these cases involve monetary payments, penalties. Therefore, a Beit Din of shelosha, of three people, would be enough. This is divrei Rabbi Meir (the opinion of Rabbi Meir), but the rabbis disagree with the opinion of Rabbi Meir. They say that the case of a Motzi Shem Ra, a person who slanders a woman and claims that she was with another man between the kiddushin and the nisuin, requires a court, a Beit Din of 23 judges, because in those cases there's also the element of capital punishment. If the wife is found guilty, we put her to death because she was with another man while she was technically engaged halakhically to her husband. So, if their witness tells us that detail and it's confirmed with eyewitnesses, that woman is put to death. Therefore, since it's a case dealing with something as severe as the death penalty, we need a higher court of 23 to deal with that situation.

