Gemara

(Mishnah): If he gave a Ma'amar and did Bi'ah, he did the Mitzvah properly.

Suggestion: This supports Rav Huna.

(Rav Huna): The proper way do Yibum is to Mekadesh the Yevamah first (with a Ma'amar).

Rejection: Perhaps the Mishnah says that this is also a proper way to do Yibum!

Objection: This is obvious!

Answer: It is not obvious;

We learned that a Ma'amar removes Zikah of Yibum and makes her like an Arusah awaiting Nisu'in. One might have thought that Bi'ah afterwards is not the Mitzvah (of Yibum, just standard Nisu'in)!

(Rav Huna): The proper way do Yibum is after being Mekadesh the Yevamah. If he did Yibum and then gave a Ma'amar, he acquired her.

Question: This is obvious, for Yibum acquired her!

Correction: Rather, (even) if he did Yibum without a Ma'amar, he acquired her.

Question (Beraisa): If he does Yibum without a Ma'amar, he is lashed. (If he acquired her, why would he be lashed?)

Answer: The lashes are only mid'Rabanan;

Rav lashes for the following:

One who is Mekadesh through Bi'ah, or in the market (in public), or without prior arrangement...

Version #1 (Chachamim of Nehardai): Rav lashes only for one who is Mekadesh through Bi'ah without prior arrangement.

Version #2: Some say that he lashes even with prior arrangement, because it is lewdness.

(Beraisa): How is Ma'amar done with a document?

Objection: Obviously, it is like Kidushin through a document! We learned that he writes to her on paper or on pottery, even if it is not worth a Prutah, 'you are Mekudeshes to me'.

Answer (Abaye): The Beraisa asks about a Kesuvah of Yibum.

Rishonim

Rif and Rosh (5:2): The proper way do Yibum is after being Mekadesh the Yevamah. If he did Yibum without a Ma'amar, he is lashed. Rav lashes for Kidushin through Bi'ah, or without prior arrangement... Some say that he lashes only for Kidushei Bi'ah without prior arrangement. Some say that he lashes even with prior arrangement, because it is lewdness.

Ran (DH Masnisin): The Mishnah means that Ma'amar and then Yibum is also proper.

Question (Chidushei Anshei Shem): It seems that the conclusion is like Rav Huna, that the Mitzvah is specifically to give a Ma'amar first!

Rambam (Hilchos Yibum 1:1): Mid'Oraisa one need not be Mekadesh his Yevamah, for Shomayim acquired her to him. He just has Bi'ah.

Rambam (2:1): Mid'Rabanan one should not have Bi'ah with her until he is Mekadesh her in front of two witnesses with something worth a Prutah. This is called Ma'amar.

Magid Mishneh: It is clear from the Gemara (52a) that a document also makes Ma'amar, like regular Kidushin.

Poskim

Shulchan Aruch (EH 166:2): Mid'Oraisa one need not be Mekadesh her. Chachamim enacted not to have Bi'ah with her until he is Mekadesh her in front of witnesses with money or a document. This is called Ma'amar.

Gra (4): Also Rashi (Kidushin 2a DH b'Vi'ah) says that a document works. Also the Gemara (Yevamos 54a) says that Bi'ah acquires totally, but money and a document do not. This implies that money and a document also acquire, just not totally. The Yerushalmi connotes that only money works.

Rema: If he was Mekadesh her with a document, also this is called Ma'amar.

Gra (5): This is b'Di'eved, like Rashi says. (In DH uv'Shtar, he says 'and if he was Mekadesh her with a Shtar...') The Rambam and Tur do not mention a document. They explain that the Gemara says that the Beraisa cannot teach about a Shtar Ma'amar, for surely if it works it is like a Shtar Kidushin! The conclusion is that Shtar does not work! This is like the Tosefta and Yerushalmi. The Rema's text of the Mechaber's Shulchan Aruch did not mention Shtar (therefore the Rema taught that it works, like the Magid Mishneh.)

Note: Also the Rif and Rosh do not mention a Shtar. BaHaG and others say that Shtar works. The Gra is the only Mefaresh I found who cites an opinion that explicitly says that Shtar does not work. Our text of the Tosefta (2:2) says that a Shtar acquires a Yevamah. The Gra does not comment in his Hagahos on the Tosefta.

Rema: She also needs Chupah after Kidushin, like other women.

Shulchan Aruch (ibid.): If he had Bi'ah without a Ma'amar, he acquired her, and he need not be Mekadesh her. He is lashed mid'Rabanan.

Rema: This is only if he had Bi'ah in front of witnesses.