To her husband

As we will explain later on, "and these three are in female form." And the Gemara will ask why it's taught in feminine form.

Our printing: And she "acquires" herself in two ways

To be within her rights to marry another

The Braisa explains in the Gemara (5b), [acquisition with money:] give her money or money-equivalent and say to her, "behold you are betrothed to me." Document: write it for her on paper, even though the paper is not worth a prutah, [say,] "behold you are betrothed to me." Through intercourse: come upon her and say "betroth me with this intercourse." All of this is learned from the [written] Torah.

Beit Shammai's reasoning is explained in the Gemara (11a)

of copper

of silver and its value is eight prutas.

To the deceased husband's widow [yavam]

To be his wife for all matters, for if he came to divorce her afterward, she does not need from him halitza rather a bill of divorce [get]. But money or a document do not have the effect of betrothing her from the Torah, rather from the Sages as they instituted an order, as they say in Yevamot. But (money or a document) do not finalize the betrothal to allow him to inherit from her or become impure for her and do not exempt from halitza, rather they make her forbidden to the other brothers.

1 . And what's the difference there--In the second chapter (41a) where it says "the man betroths himself or with his agent," let it say here: the woman becomes betrothed

2. Because it needs to teach money--that with [money] we aquire, and we said previous (4b) "from where do we know that we can acquire with money," and we explain that we learn "take" "take" from the Field of Efron that we consider it an acquisition. Therefore we learn here that [money] can acquire.

And from where do we derive that [betrothal is accomplished by means of giving] money? - It is not here where [the Gemara] is asking [about the source for betrothal by money], but rather later on [Kiddushin 3b:4]. Here it is being used [in the course of] an explanation for the entire matter [at hand, namely]: because he wanted to teach [about betrothal through] money, and from where do we derive that [betrothal is accomplished by means of giving] money? We will derive it later on [Kiddushin 4b:3] from "taking." Since "taking" is a term for acquisition, the Mishna uses the expression "a woman is acquired."