Yevamos, chapter five, mishnah 1. This chapter deals with four acts that a man can perform with his yevamah, and with how these acts interact with one another. Let us begin, then, by defining the four acts.
The four acts:
Biah - actually performing the yibum.
Chalitzah - which releases the yevamah from the zikah, the bond between her and the yavam.
Ma'amar - a rabbinic form of kiddushin. The proper order is ma'amar and then yibum; however, even if the yavam decided not to complete the marriage through yibum and performed chalitzah instead, the ma'amar itself requires a get, since it is a form of rabbinic kiddushin.
Get - this is the novel point presented by our mishnah: giving a get to the yevamah, even without any yibum or chalitzah having preceded it.
What is the effect of giving such a get? Several things are accomplished by it:
It disqualifies the yevamah from undergoing yibum, both with the one who gave the get and with the other brothers.
Since a get was given where there was a bond of yibum, the Sages said that the yavam is forbidden to her relatives, just like all the relatives who are forbidden to a man on account of his divorcee.
She becomes disqualified from marrying into the kehunah, like a divorcee.
It turns out that this get carries all the disadvantages of a get, without even its one advantage: it does not permit her to marry another man, and she still requires chalitzah. This get is entirely a rabbinic institution.
The view of Rabban Gamliel:
The mishnah comes to discuss the relationship between these acts, and it opens with the words "Rabban Gamliel omer: ein get achar get" - Rabban Gamliel says: there is no get after a get. That is, a yavam who gave a get to his yevamah and afterward gave a get to her co-wife, the second widow of his brother, the second get does not take effect and is not considered a get at all: it does not disqualify her from the kehunah, and the yavam is not forbidden to her relatives. Once one get has been given, the second get accomplishes nothing.
The same is true of the other acts, in Rabban Gamliel's view:
There is no ma'amar after a ma'amar - if he made a ma'amar with one of the two yevamos, the second ma'amar accomplishes nothing and does not require a get, as though it had never been done at all.
There is no biah after a biah - if he had relations with the yevamah and thereby performed yibum, and afterward had relations with her co-wife, or another brother had relations with that same woman, the second act of relations has no halachic force whatsoever, and is nothing but a forbidden relationship.
There is no chalitzah after a chalitzah - once one widow has undergone chalitzah, the second chalitzah accomplishes nothing, and the yavam is not forbidden to the relatives of the second woman by the law of the relatives of a chalutzah.
It is worth noting that this law applies not only where there are two co-wives, two widows, but even where there is one widow and two yevamim, two brothers: if one of them gave a get, the second get accomplishes nothing; and if one of them made a ma'amar, the second ma'amar accomplishes nothing.
The view of the Sages:
The Sages disagree with Rabban Gamliel regarding two of the four cases, and hold that the second get does take effect, is considered a get in every respect, and brings about all the negative consequences that a get carries with it; and likewise the second ma'amar takes effect and requires a get. In the other two cases, however, they agree with Rabban Gamliel: with relations and with chalitzah, once one has been done, no further act of relations or chalitzah accomplishes anything.
In summary: in this mishnah we learned the four acts that a man performs with his yevamah - biah, chalitzah, ma'amar and get - and the nature of a get given to a yevamah, which is entirely rabbinic: it disqualifies her from yibum, forbids her relatives to him and disqualifies her from the kehunah, and nevertheless does not exempt her from chalitzah. We also examined the dispute between Rabban Gamliel and the Sages: according to Rabban Gamliel, no second act takes effect after the first in any of the four cases, while the Sages distinguish between them and rule that the second act does take effect with a get and with a ma'amar, agreeing with him regarding relations and chalitzah.