Gemara

(Beraisa - R. Meir): If a woman ate, walked haughtily, or nursed a baby in the market, her husband must divorce her (lest she had or will have Bi'as Zenus);

R. Akiva says, he need not divorce her until she becomes the subject of gossiping women.

R. Yochanan ben Nuri: If so, anyone who hates a woman can break up her marriage by starting rumors. The Torah requires divorce only due to "Ervas Davar (infidelity)"! We learn a Gezeirah Shavah from "according to two or three witnesses a Davar will be established." Solid evidence is required.

90a (Mishnah - Beis Shamai): One may divorce only if "he found in her Ervah";

Beis Hillel say, even if she burned the food, he may divorce her - "he found in her Ervas (or) Davar (a matter)";

R. Akiva permits even if he found a prettier woman - "if she does not find grace in his eyes."

Beis Shamai explain "she will not find grace in his eyes Ki (because) he found Ervah in her." R. Akiva explains "whether she will not find grace in his eyes, (or) Ki (if) he found Ervah in her."

Question (Rav Papa): If he found neither Ervah nor a Davar and divorced her, what is the law?

Answer (Rava): One who raped a virgin "may not divorce her his entire life." If he divorced her, his entire life he must remarry her. Here, it does not say that he must remarry her.

(Beraisa - R. Meir): If one sees his wife go out with uncovered hair, weave in public with her elbows exposed, or bathe where men bathe, it is a Mitzvah to divorce her - "he found in her Ervah... he sent her from his house."

(Rav Yehudah): "Ki Sanei Shalach" - one who hates his wife should divorce her;

(R. Yochanan): This teaches that one who divorces his wife is hated.

They do not argue. R. Yochanan discusses one's first Zivug, and Rav Yehudah discusses his second.

(R. Elazar): The Mizbe'ach cries over one who divorces his first wife - "the Mizbe'ach cries... for you betrayed your companion, the wife of your covenant."

Yevamos 63b (Rava): It is a Mitzvah to divorce an evil wife - "expel the scoffer and cease quarrels."

Rishonim

Rif and Rosh (9:15): We learn from Rava that l'Chatchilah, one who found neither Ervah nor a Davar should not divorce. It is a Mitzvah to divorce an evil wife - " expel the scoffer and cease quarrels."

Rambam (Hilchos Gerushin 10:21): One should not divorce his first wife unless he found in her Ervas Davar - "he found in her Ervas Davar". It is improper to be quick to divorce her. If he hates his second wife, he should divorce her.

Question (Beis Shmuel EH 119:3): This is like Beis Shamai, who permit only due to Ervah! Also, if he found Ervah, he should rush to divorce her! Rather, the Rambam cites the verse (and the Shulchan Aruch cites the Rambam), but he means Ervah or a Davar. For a Davar, one should not rush to divorce.

Rambam (22): If a woman has bad tenets and is not modest like proper Bnos Yisrael, it is a Mitzvah to divorce her - " expel the scoffer and cease quarrels."

Poskim

Shulchan Aruch (EH 119:3): One may not divorce his first wife unless he found in her Ervas Davar.

Beis Yosef (DH Ki): The Rif and Rosh did not explicitly rule like Beis Hillel. They rely on the reader to understand that we follow them against Beis Shamai and against R. Akiva. The Rambam explicitly ruled like Beis Hillel.

Beis Shmuel (2): The Tur and Shulchan Aruch hold that Beis Hillel and Beis Shamai argue about Zivug Sheni. The verse "...Ervas Davar" refers to Zivug Sheni. All forbid divorcing Zivug Rishon due to a Davar other than Ervah. Rashi connotes that they argue about Zivug Rishon. One may divorce due to a Davar, but Hash-m despises it. Perhaps the Tur agrees that they argue about Zivug Rishon, but since the Mizbe'ach cries over this, it is improper to do so. If he did not find Ervah or Davar, we force him not to divorce and transgress the Torah. One may divorce b'Al Korchah due to Davar or Ervah.

Rema: If he did not find Ervah, the Mizbe'ach cries over one who divorces his first wife. This applies to when one could divorce b'Al Korchah (against her will). One may divorce with her consent.

Beis Yosef (DH ba'Meh): The Agudah says that the Mizbe'ach cries only when he divorces b'Al Korchah.

Darchei Moshe ha'Aruch (YD 228:28 DH Od): There is no speck of sin to divorce her if she does not want to remain with him.

Shulchan Aruch (ibid.): It is improper to be quick to divorce his first wife. If he hates his second wife, he should divorce her.

Chelkas Mechokek (2): First, the Shulchan Aruch forbade divorcing Zivug Rishon without Ervah or Davar; the Navi bewails this. Here, the Shulchan Aruch calls it merely improper to rush to do so! Perhaps here it refers to with her consent. Alternatively, if one witness testified about Ervah, he should not rush to believe him.

Taz (4): One who sees immodesty in his first wife should not rush to divorce her. Perhaps she will regret it and change. One who sees immodesty in his second wife should immediately divorce her.

Question: Beis Hillel permit divorcing for a Davar even without hatred!

Answers #1,2 (Chelkas Mechokek 3): The Shulchan Aruch teaches that it is improper to divorce unless he hates her. Alternatively, it teaches that one should divorce if he hates her even if she did nothing improper. Beis Hillel discuss hatred due to a Davar, for this is the normal case.

Answer #3 (Beis Shmuel 4): One may divorce Zivug Rishon only if there is hatred due to a Davar. One may divorce Zivug Sheni due to hatred, even without a Davar.

Shulchan Aruch (4): If a woman has bad tenets and is not modest like proper Bnos Yisrael, it is a Mitzvah to divorce her.