Gemara

R. Meir forbids marrying Me'uberes or Meinekes Chavero (a woman pregnant with or nursing another man's baby). If he did, he must divorce her and may never remarry her;

Chachamim say, he may not marry her. If he did, he must divorce her. When the period of nursing finishes, he may remarry her.

Kesuvos 60a (Beraisa - R. Meir): If a woman was widowed during the 24 months of nursing, she may not become Mekudeshes or have Nisu'in until 24 months (lest she become pregnant and wean the baby prematurely).

Yevamos 42a (Beraisa): If a woman gave her baby to a wet-nurse or weaned him, or he died, she may marry immediately.

Rav Papa and Rav Huna brei d'Rav Yehoshua were about to permit a woman due to this Beraisa. A woman told them that Rav Nachman forbade her to marry in such a case.

Question: Rav Nachman permitted widows of the house of the Reish Galusa (Exilarch)!

Answer: They are different. A wet-nurse who accepted to nurse a baby of their house would not retract.

(Rav Papi): We have another source that Rav Nachman forbids!

(Beraisa - R. Meir): A woman must wait three months before remarrying even if surely she is not pregnant, e.g. she was sterile, an Ailonis, a minor...

R. Yosi permits her to marry immediately.

(Rav Nachman): The Halachah follows decrees of R. Meir.

Retraction (Rav Papa and Rav Huna): We overlooked this.

The Halachah is, if the baby died, she may marry. If she weaned him, she must wait.

(Mar bar Rav Ashi): Even if he died, she must wait. If not, perhaps she will kill her baby in order to marry! Such a case occurred, and a woman choked her baby!

Rejection: That woman was insane. A normal woman would not kill her baby.

Rishonim

Rif and Rosh (Kesuvos 25a and 5:20): the Halachah follows R. Meir, who forbids a nursing widow to marry for 24 months. This is even if she gave the baby to a wet-nurse or weaned him. If he died, she is permitted.

Ran (DH Oh Gamalto): Some permit a woman from a family (prominent) like the Reish Galusa who gave her child to a wet-nurse, or any woman, if the wet-nurse swore to nurse for the entire period. I disagree. Rav Papi dissuaded Rav Papa and Rav Huna from permitting such a case, for the Halachah follows decrees of R. Meir, e.g. Havchanah (a widow or divorcee must wait three months before remarrying, to avoid doubts about from whom she is pregnant) when she cannot be pregnant. Here also, we forbid in every case! The Reish Galusa was different, for he was so famous. Rav Nachman was not refuted. Why did the Rif and Rambam omit the Heter of the Reish Galusa? Perhaps it is because nowadays there are no such families.

Rambam (Hilchos Gerushin 11:27): Even if a woman gave her baby to a wet-nurse or weaned him within 24 months, she may not remarry. If the baby died, she may marry. We are not concerned lest she kill her baby.

Magid Mishneh: The Rashba (723) forbids even a woman of the Reish Galusa's house if she nursed until the baby recognizes her, lest he not nurse from another.

Rosh (Kesuvos 5:20): The Reish Galusa's house was powerful. Rav Nachman permitted such women after they hired wet-nurses, for no one could retract. People knew that they are different, and would not permit other women. We do not permit other women even if the wet-nurse swore or vowed Al Da'as Rabim not to retract, lest people permit other women without an oath or vow. We permit one who weaned her baby before her husband died. We do not decree lest we permit one who weaned after death. (This is forbidden lest she rush to wean him, which is dangerous.) If we would decree, we should also decree about women of the Reish Galusa's house! We permit also one whose breasts dried and she never nurses, or her milk ceased and she hired a wet-nurse before her husband died.

Beis Yosef (EH 13 DH v'Zeh and DH v'Chosav Od): Ri ha'Zaken forbade even if the wet-nurse gives a huge security so she will not retract. Others do not hear about this; they might permit without a security. The Rivash forbids even if this might lead her to sin. This does not warrant uprooting the enactment. A Chacham once relied on a vow Al Da'as Rabim to permit, for this is like Rav Nachman's Heter. All Chachmei Ashkenaz forced him to retract. The Maharam me'Rotenburg said that if the Halachah followed Rav Nachman, the Gemara would have brought his Heter, and it would not need to say that death of the baby permits! The Rif omitted Rav Nachman's Heter.

Poskim

Shulchan Aruch (EH 13:11): Chachamim decreed not to be Mekadesh Me'uberes or Meinekes Chavero until the baby is 24 months old.

Chelkas Mechokek (9): Shiduchin (arranging a future marriage with her) is permitted only if the man will swear not to enter her house until after the 24 months, like we say about Havchanah in Sa'if 1. The Beis Yosef learns about Havchanah from Teshuvas ha'Rosh about Me'uberes Chavero.

Shulchan Aruch (ibid.): Even if she gave her baby to a wet-nurse or weaned him within 24 months, she may not marry, even if the wet-nurse swore or vowed Al Da'as Rabim not to retract, and even if she swore to an important man who walks in the king's courtyard.

Rosh (Teshuvah 18:17, cited in Beis Yosef DH u'Mah she'Chosav Rabeinu): Rav Nachman permitted only for the Reish Galusa's house. They descended from the king and ruled over Yisrael, and they were feared like kings. Nowadays, even if a Yisrael finds grace in the eyes of the king, people do not fear him very much.

Beis Shmuel (24): Securities or a second wet-nurse do not permit.

Shulchan Aruch (ibid.): She may marry in the following cases: the baby died; she weaned him before her husband died; she never nurses, e.g. she has dry breasts; her milk ceased and she hired a wet-nurse before her husband died; she hired a wet-nurse three months before her husband died, and did not nurse her baby in these three months.

Chelkas Mechokek (10): This connotes that if she did not nurse for three months she is permitted even if her breasts did not dry up. However, the Rosh (53:3) says that breasts dry up after three months without nursing! Rather, we permit whenever her breasts dried up, even if she caused this.

Ran (Teshuvah 12, cited in Beis Yosef DH v'Zeh): A Gaon forbids her only when this helps the baby. We are not concerned for one woman in 1000 who can resume nursing after three months cessation. We may rely on this for an Isur mid'Rabanan.

Rivash (360, cited in Beis Yosef DH u'Mah she'Chosav Rabeinu v'Im): We forbid if her milk ceased after she was widowed, lest women cause milk to cease through potions or bad foods.

Beis Shmuel (26): Hiring a wet-nurse does not permit by itself. If it did, there would be no need to teach when her milk ceased, for surely she hired a wet-nurse!

Question (Liskas ha'Sofrim, in Shulchan Aruch Rosh Pinah): Perhaps her milk ceased and she will buy milk and eggs for the baby!

Shiltei ha'Giborim (Kesuvos 25a:1): The Rosh (53:4), Tur and Rivash (462) forbid Meinekes Chavero even if she never nursed her baby yet. Some are lenient.