Still catching up on posting thoughts on the Daf. For those who are less text-oriented, jump down to My Noachide Wedding.
The gemara here mentions Levi bar Darga redeeming his daughter from captivity for 13,000 gold coins. Note my comments here (Nedarim 25a) and here (Nedarim 41), about thirteen being a number used in the gemara for exaggeration, for effect.
Our gemara talks about not paying too much to ransom captives. Tosafot דלא here asks the classic question regarding talmudic cases in which overly large sums were paid, and gives three answers which shape, to this day, our policy in issues like prisoner exchange: Greater expenditures are justified, potentially, if one is redeeming his wife/himself, or if one is redeeming a person who is exceptionally valuable for society, or if one is in an environment where capturing/ransoming is normal, so that one is not really risking additional kidnapping by acceding to a demand.
See Rashi here on מין. Here Rashi says “min” means “one who cleaves to idolatry, like a priest.” See also Rashi to Sanhedrin 38a, where Adam haRishon is accused of being a “min.” See also Rashi to Shabbat 116a ספרי מינין. See also Rashi Berachot 12a "Minim", and Rashi Shabbat 75a. However, Rashi Berachot 12b מינות says “those who convert the logic of Torah to erroneous analysis and idolatry.” (Note the censored edition there, though, which may explain this comment in Rashi.)
Tosafot כיון is very important, explaining the justifications for honoring the deal struck between the Jews and the Givonim after entering Israel.
Fascinating, from a methodological perspective: The gemara here translates talmudic use of the word רבים based on biblical use of the word רבים!
See Tosafot הנודר explaining why taking a vow is like building an illegal altar.
Rashi here המוכר שדהו לפירות says that Yovel ceased after the initial exile of Reuven and Gad. Tosafot Gittin 36a “b’Zman” and Tosafot Erchin 31b/32a Hitkin disagree, arguing that they had Yovel in the second Beit haMikdash. Tosafot has substantial proof on his side. Ramban to Gittin 36a disagrees with him, though.
See the important Tosafot ור' שמעון, pointing out that we are free to analyze the reasons for/lessons from mitzvot (דורש טעמא דקרא); the only debate regarding the legitimacy of this approach is regarding using those reasons/lessons for practical halachic decisions.
The gemara here points out that we wish to encourage lending; this is because loans are the premier engine for tzedakah in a Torah society. See my comments in “Government as Economic Protector.”
Rashi and Tosafot disagree as to the meaning of משום חינא. Rashi’s view seems to say that we are trying to provide a woman with an incentive to marry a man, whereas Tosafot explains that we are trying to make it easier for her to find a husband.
The gemara here indicates that marriage is a mitzvah.
See Beitzah 36b-37a, where marriage is a mitzvah only if one does not currently have a wife and children. From there it is clear that marriage is, at most, a mitzvah-enabler (for permissible procreation) but not a mitzvah in itself.
However, the Rambam (Mishneh Torah Hilchot Ishut 1:2) says marriage is, indeed, a mitzvah. See the Magid Mishneh there and in Hilchot Ishut 1:4, who tries to explain this as either a copyist's error or a reference to a prohibition against living together without marriage.
See also the Rosh to Ketuvot 1:12, on the berachah we recite for kiddushin not being a birkat hamitzvah.