We begin our study of the first Mishnah in the second chapter of Maseches Kiddushin. The Mishnah opens: "Ha'ish mekadesh bo uvishlucho" - a man may betroth a woman and marry her himself, directly, and he may also appoint an agent and tell him: "Go take this money and betroth this woman for me."
"A mitzvah through oneself rather than through an agent":
The Mishnah places "himself" before "his agent," and from this precise wording the Gemara derives two points:
A mitzvah is better performed by oneself than through an agent - it is a greater mitzvah to perform the act oneself rather than through an agent, in order to show affection and importance for the mitzvah.
The prohibition against betrothing a woman without seeing her - there is another opinion, that the reason a person is mentioned before his agent is to teach that one may not betroth a woman without first seeing her. This does not mean that one may not see her and only afterward appoint an agent; rather, mentioning the person himself first indicates that this is one of the requirements.
The betrothal of a woman and the betrothal of a daughter:
Just as it was said of the man "himself or through his agent," so too the Mishnah says: "Ha'ishah miskadeshes bah uvishlucha" - she too may become betrothed herself, or appoint an agent to receive the betrothal on her behalf.
The Mishnah continues: "Ha'ish mekadesh es bito k'shehi na'arah, bo uvishlucho" - a father may betroth his daughter while she is a na'arah, that is, during the six months following her reaching maturity, and this too either himself or through an agent.
Why did the Mishnah specify "na'arah," when by law the father may betroth her even while she is a minor? The Mishnah comes to teach us proper conduct: even though halachically he has the ability to marry off his daughter while she is a minor, before she has reached the age of mitzvos, it is not fitting to do so. The daughter should be old enough to express her opinion and say that she wishes to marry this particular young man, something she is incapable of doing while she is a minor.
"Hiskadshi li b'tamar zu":
The Mishnah continues and distinguishes between two forms of statement, in a case where a man holds several dates - pieces of food, each of which may be worth a perutah:
"Hiskadshi li b'tamar zu, hiskadshi li b'zu" - "if one of them is worth a perutah, she is betrothed; and if not, she is not betrothed." Since he stated separate acts of betrothal, it is enough that one of them alone is worth a perutah, for each and every one is an independent act of betrothal.
"B'zu uv'zu uv'zu" - "if all of them together are worth a perutah, she is betrothed; and if not, she is not betrothed." Here he betroths her with all the dates together, and therefore we combine them all: if together they are worth a perutah, she is betrothed, and if even together they are not worth a perutah, she is not betrothed, because a single act of betrothal was performed here with a group of pieces of food.
"If she was eating them one after another":
In the case where he said to her "with this one and this one and this one," which is a single act of betrothal made up of several parts, the Mishnah adds: what will be if, as he hands her one date after another, she eats each one immediately, so that by the time they reach the last date she has already eaten all the rest? To this the Mishnah says: "Einah mekudeshes, ad sheyehei b'achas mehen shaveh perutah" - she is not betrothed unless one of them is worth a perutah.
The Gemara explains that "one of them" does not mean whichever one it may be, but specifically the last of them - that is the one that must be worth a perutah. The reason is this: since she ate the dates as they were being given, even if the earlier ones were worth a perutah, the betrothal is not completed until he has finished giving her all of them, for he is betrothing her with all the dates together. It emerges that the dates she ate before the completion of the betrothal have the status of a loan - a debt that she owes him, since the betrothal had not yet been completed and she had already eaten them.
It follows that when these dates are included in the betrothal, he is betrothing her with a loan. And the halachah is that if a woman owes a man money, and he says to her: "With the money you owe me I hereby betroth you" - this is not a valid betrothal, because he is giving her nothing at the time of the betrothal. Here too he is not giving her anything, since she already owes him for those dates until the betrothal is completed. Therefore it is the last date that must be worth a perutah, so that the betrothal should take effect.
This Mishnah follows the view regarding one who betroths a woman with a loan and a perutah - and this is precisely our case, for he is saying to her: with those earlier dates, which have the status of a loan, and with this perutah, I hereby betroth you - she is betrothed, because her mind in the betrothal is focused primarily on the perutah being given to her now, and therefore this is a valid betrothal.
In summary: In this Mishnah we learned that a man betroths either himself or through an agent, and from the fact that "himself" precedes "his agent" we learn that "a mitzvah is better performed by oneself than through an agent," and also that one may not betroth a woman without seeing her. We also learned that a woman becomes betrothed either herself or through an agent, and that a father betroths his daughter when she is a na'arah - from which we derive the proper conduct of not marrying her off while she is a minor. In the second part of the Mishnah we examined the distinction between "be betrothed to me with this one, be betrothed to me with this one," which are separate acts of betrothal and where a perutah in one of them suffices, and "with this one and this one and this one," which is a single act where all of them are combined. And finally, where she was eating them one after another, it emerges that the earlier ones have the status of a loan, and therefore specifically the last one must be worth a perutah - and this follows the view concerning one who betroths with a loan and a perutah, that her mind is on the perutah.