Welcome to Maseches Kiddushin, chapter 1, mishnah 1. This mishnah discusses how a woman becomes betrothed and how she leaves the marriage bond, and likewise how the bond between a yevamah and her yavam is created and how she is released from that bond. The remaining mishnayos in the chapter go on to discuss how other acquisitions are made and how those acquired go free.
"HaIshah niknis bishalosh derachim v'konah es atzmah bishtei derachim" - a woman is acquired in three ways and acquires herself in two ways:
The woman - meaning the woman being married - is acquired to her husband by one of three ways, and she leaves the bond ("acquires herself") by one of two ways. These are the three ways of acquisition:
"BeKesef" - by giving money, and jewelry also serves as a form of money.
"BiShtar" - he writes to her in a document, "Behold you are betrothed to me with this," and even if the document itself has no value of a perutah, the document is effective.
"UveViah" - marital relations between them, when done for the purpose of betrothal, is also one of the forms of betrothal.
The amount of money:
The mishnah specifies what sum counts as money for this purpose: "BeKesef - Beis Shammai omrim: bedinar uveshaveh dinar, uVeis Hillel omrim: biperutah uveshaveh perutah" - with money: Beis Shammai say a dinar or the value of a dinar, and Beis Hillel say a perutah or the value of a perutah.
Beis Shammai: a dinar or the value of a dinar. The coin itself is not required; it is enough to have something worth at least a dinar, which is a quarter of a sela - a quarter of a Torah shekel.
Beis Hillel: an actual perutah or the value of a perutah - a far smaller sum.
From here comes the custom that the one officiating at the betrothal asks the witnesses about the ring: "Does it appear to you to be worth a perutah?" - and almost every ring meets this measure.
And what is the measure of a perutah? "Vechamah hi perutah? Echad mishmonah be'issar ha'Italki" - one eighth of an Italian issar. The issar itself is one twenty fourth of a dinar, so a perutah works out to be one one hundred and ninety second of a dinar. This is the gap between Beis Shammai's measure of a dinar and Beis Hillel's measure of a perutah or the value of a perutah.
How a woman leaves the marriage:
"V'konah atzmah beget uvemisas haba'al" - by one of these two ways she leaves the marriage: with a get, or through the death of the husband.
The yevamah - how she is acquired:
A yevamah is a woman whose husband died without children, and she falls to yibum before her husband's brother. "Yevamah niknis beviah" - from the Torah this is the only way in which the mitzvah of yibum is fulfilled with her. However, the Rabbis created a form called 'kiddushei ma'amar', a rabbinic betrothal that, as it were, precedes relations with the yevamah.
How the yevamah leaves the bond:
The intent of the mishnah must be understood precisely: the question is not how the yevamah goes out after the yavam has already had relations with her, for from that moment they are like husband and wife, and she goes out with a get or through the death of her husband like any other woman, as was taught at the beginning of the mishnah. The mishnah's question concerns leaving the bond of yibum itself, while she is still awaiting the yavam and waiting for the mitzvah of yibum to be performed with her. In this there are two ways:
"V'konah es atzmah bachalitzah" - the yavam performs chalitzah with her, and through this she acquires herself and leaves the bond without yibum.
"Uvemisas hayavam" - if the yavam died, assuming there are no other brothers and no other yavam available, or that all the yevamim died, she leaves the bond, since there is no one left to fulfill the mitzvah of yibum with her.
In summary: in this mishnah we learned the three ways a woman is acquired - money, a document and marital relations, the dispute between Beis Shammai and Beis Hillel about the amount of money and the measure of a perutah, the two ways of leaving the marriage - a get and the death of the husband, and also the acquisition of a yevamah through relations and her release from the bond through chalitzah or the death of the yavam.
In the coming mishnayos of the chapter we will deal with the other acquisitions - how they are acquired and how they go free.