Gemara

55a (Mishnah): R. Yochanan ben Gudgada testified that a Chereshes (deaf woman) who was married mid'Oraisa may be divorced.

(Rava): This teaches that if a man told witnesses 'watch me give this Get', and told his wife (before giving it) 'take this loan document', she is divorced;

Divorce works even if she has no understanding. The same applies here!

One might have thought that since he said 'take this loan document', he invalidated the Get. Rava teaches that this is not so. Had he invalidated it, he would have told the witnesses. Since he did not tell them, it is still valid. He deceived his wife to spare himself shame.

78a (Mishnah): If one told his wife 'take this loan document' (and gave a Get to her), or she found her Get in back of him, and read it and realized that it is her Get, she is not divorced unless he says 'this is your Get';

If he put it in her hand while she was sleeping, and she woke up and found her Get in her hand, it is Pasul unless he says 'this is your Get.'

Question: Why does it help to say 'this is your Get'? He did not give it to her! If one told his wife to take her Get from the floor, she is not divorced!

Answer: The case is, he bent his waist towards her to bring the Get closer to her, and she took it from his belt.

(Beraisa - Rebbi): If he told her 'take this loan document', or she took the Get from his belt, and found that it is her Get, she is not divorced unless he says 'this is your Get';

R. Shimon ben Elazar says, the Get is only valid if he takes it back and gives it again and says 'this is your Get.'

If he put it in her hand while she was sleeping, and she woke up and found her Get in her hand, it is not a Get unless he says 'this is your Get';

R. Shimon ben Elazar says, it is valid only if he takes it back and gives it again and says 'this is your Get.'

The Beraisa needed to teach both cases. Had it taught only the Reisha, one might have thought that there Rebbi does not require giving the Get again, because she was able to be divorced when she got it, but if he gave it to her when she was sleeping, Rebbi would agree that he must give it again.

Had it taught only the Seifa, one might have thought that R. Shimon would agree in the Reisha that he need not give it again, because she was able to be divorced when she got it.

Rishonim

The Rif and Rosh (26b and 5:14) bring the Gemara on 55a verbatim.

The Rif and Rosh (40a) brings the Mishnah on 78a.

Ran (DH Masnisin): We must say that they were discussing divorce. If not, even if he gave it silently, without saying that it is a loan document, she would not be divorced. When discussing divorce, if he properly gave it silently she is divorced, but not if he merely bent his waist towards her.

Rambam (Hilchos Gerushin 1:10): If a man told witnesses 'watch me give this Get', and told his wife 'take this loan document', it is Kosher, for he told the witnesses that he gives it b'Toras Gerushin. He told his wife that it is a loan document to spare himself shame.

Rambam (10:23): One can divorce his wife if she became deaf. If she became insane, he may not divorce her until she regains sanity. This is an enactment lest she be Hefker for immoral men, for she cannot guard herself. If he divorced her, she is divorced. He expels her from his house, and need not deal with her again.

Ra'avad: She is divorced only if she can guard her Get.

Magid Mishneh: The Gemara says so explicitly. The Rambam agrees. He relies on what he wrote above (2:9), that if a girl cannot distinguish between her Get and something else, which is the same as 'cannot guard herself', she can be divorced only if her father gets the Get (if there was no Nisu'in yet).

Rosh (8:4): One who is sleeping has no Da'as at all. She is worse than a Chereshes. The Ramah says that if the Get is not in her hand when she wakes up, he must take it back and give it again and say 'this is your Get'. This seems correct, for the first giving is invalid, since it fell from her hand when she awoke.

Poskim

Shulchan Aruch (EH 119:6): One can divorce a woman without her Da'as. Therefore, a minor can be divorced even though she does not have full Da'as.

Beis Yosef (DH Lefichach): This is only if she can distinguish between her Get and something else.

Shulchan Aruch: This is even if her father accepted Kidushin for her and she is married mid'Oraisa. The same applies to a healthy woman who became deaf. If she became insane he may not divorce her until she regains sanity, lest she be Hefker for men. If he divorced her, she is divorced only if she can guard her Get.

Rema: Some say that even b'Di'eved she is not divorced.

Shulchan Aruch (EH 136:5): One must give a Get b'Toras Gerushin. If he gives it in the guise of a loan document she is not divorced unless he tells her later that it is her Get, or told the witnesses beforehand.

Beis Yosef (DH v'Tzarich): "Sefer Kerisos v'Nosan b'Yadah" teaches that it must be given b'Toras Sefer Kerisos.

Tur: She must know when she gets it that it is her Get, and she receives it to be divorced. If he gave it in the guise of a loan document, she is not divorced unless he tells her later that it is her Get, or he told the witnesses beforehand.

Question (Beis Yosef, ibid.): This is not precise. Even if she did not know at the time, it helps if he tells her later, or told witnesses beforehand! Rather, the Tur means that he must give it b'Toras Gerushin.

Answer #1 (Drishah (2): The Tur discusses when they were discussing divorce. Therefore, if he gives it silently she knows that it is her Get, but not if he told her that it is a loan document.

Answer #2 (Bach): Tosfos (78a DH Eino) says that if he told witnesses beforehand, it is Kosher because they will tell her and she will not return to him. The Tur teaches that l'Chatchilah she must know at the time she gets it, lest he forget to tell her later or the witnesses will not tell her.

Answer #3 (Taz 2): Either she must know by herself that it is her Get, e.g. by reading it, or that he informs her. Knowing by herself helps only at the time it is given. If she did not know then, then he must tell her or witnesses.

Rema: She must know that it divorces her, or the witnesses must tell her later.

Beis Shmuel (3): Tosfos (78a DH Eino) says so. The Rema should not write this as if he explains the Shulchan Aruch, for the Rambam and Tur do not require that they tell her.