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Beis Shamai says that a person may not divorce his wife unless she was Mezaneh.
Beis Hillel holds that one may divorce his wife for burning the food and R. Akiva holds he may divorce her even if he finds another woman who is nicer looking.
A woman is only forbidden to her husband is if there are two witnesses that she was Mezaneh.
Reish Lakish says the word Ki in the Torah means one of four things; if, maybe, except, and because.
If a person rapes a girl he must marry her and he may never divorce her; if he divorces her he must remarry her.
According to Beis Shamai if someone divorced his wife even though she was not Mezaneh he does not have to remarry her.
A person may not stay with his wife if he has already made the decision to divorce her.
If a woman acts licentiously it is a Mitzvah Min ha'Torah to divorce her.
If a person marries a woman who was divorced because of licentious behavior if he is Zocheh he will divorce her but if he is not Zocheh she will bury him.
A person who divorces his first wife is hated but a person may divorce his second wife if he hates her.
When a person divorces his first wife even the Mizbe'ach drips tears.
A BIT MORE
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TOO MUCH MODESTY
Beis Shamai says that a person may not divorce his wife unless she was Mezaneh, while Beis Hillel holds that one may divorce his wife for burning the food. The Chasam Sofer explains the Gemara in Maseches Shabbos which states that Beis Shamai was a Kapdan and Beis Hillel was a lover of people who ran after Shalom and brought people closer to Torah. The explanation of that Gemara is not that Beis Shamai was more of a Kapdan than he rather Beis Hillel was humble to the extreme. Why was Hillel humble to an extreme? He learned this characteristic from Hashem Yisbarach Who permits His name to be erased in the water in order to allow a Sotah to stay with her husband. Even though the husband can just as well divorce her and alleviate the need to erase the name of Hashem, even so Hashem Yisbarach allows His name to be erased. If so certainly a mortal human being must forfeit his own honor in order to bring Shalom. However, Beis Shamai cannot learn out the same Din because he holds that it is forbidden to divorce a wife unless there are witnesses that she was Mezaneh, so therefore the option to divorce a Safek Sotah does not exist.
If a woman harbors warped views and she is not modest in the manner of a Kosher Bas Yisrael, it is a Mitzvah to divorce her. A Kosher person should not marry a woman who was divorced as a result of her immodest ways because it is not appropriate that one person expels a Reshi'ah from his house and a second person takes her in. (Rambam Hilchos Gerushin 10:22)
Index to Revach for Maseches Gitin