Gemara

Beraisa - R. Yosi: Hash-m's ways are unlike the ways of people! If Reuven angers Shimon, Shimon seeks to financially ruin him and constantly vex him. Hash-m cursed the snake and caused that the snake finds his food wherever it is, be it on the roof or on the ground.

Hash-m cursed (Ben Yehoyada - agreed to Noach's curse of) Kena'an (that his descendants would be slaves). Kena'an eats and drinks like his master.

Hash-m cursed women (to be unable to express their desire for their husbands). He caused that men (have great desire to) chase women.

Hash-m cursed the ground. He caused that everyone is fed from it.

87a: If someone sinned against R. Zeira, R. Zeira would pass in front of him to give him an opportunity to ask forgiveness.

A case occurred, a butcher offended Rav and did not come to ask forgiveness on Erev Yom Kipur. Rav decided to go to him. Rav Huna remarked that this will cause the butcher to die (if he has an opportunity to ask forgiveness and does not do so).

When the butcher saw Rav he said 'Go! I have nothing to do with you'. The butcher was chopping bones. A bone came off and hit him in the neck and killed him.

Once, Rav offended R. Chanina. For 13 years Rav went to him on Erev Yom Kipur to appease him; R. Chanina was not appeased.

Question: Why did R. Chanina refuse to forgive him? Rava taught that if one is Ma'avir Al Midosav (does not punish others who acted improperly towards him), all his transgressions are overlooked!

Answer: R. Chanina was Rosh Yeshiva (in Eretz Yisrael). In a dream he saw that Rav would become Rosh Yeshiva. Therefore, he refused to forgive him, forcing Rav to go to Bavel (and become Rosh Yeshiva there).

23a - R. Yochanan: If a Chacham does not bear a grudge (for Tza'ar ha'Guf, e.g. verbal abuse) like a snake, he is not a proper Chacham.

Objection: This is forbidden!

Beraisa: "V'Ohavav k'Tzeis ha'Shemesh bi'Gvuraso" - this is one who is disgraced and does not disgrace; people shame him and he does not answer...

Answer: A Chacham bears a grudge in his heart.

Rosh Hashanah 17a - Rava: If one is Ma'avir Al Midosav, all his transgressions are overlooked.

We learn from "Nosei Avon v'Over Al Pesha" - Hash-m bears the sin of one who overlooks others' transgressions.

Rav Huna brei d'Rav Yehoshua fainted. When he recovered, he said 'death had been decreed on me. Hash-m said that since I do not return to others like they mistreat me, so will be done to me.'

Ta'anis 25b: A case occurred, during a fast for lack of rain R. Eliezer said Shemoneh Esre with the six additional Berachos. He was not answered. R. Akiva came in front of the Aron and said 'Avinu Malkeinu...' and rain came. People started murmuring (that R. Akiva is greater than R. Eliezer his Rebbi).

A Bas Kol: R. Akiva is not greater. Rather, he is Ma'avir Al Midosav and R. Eliezer is not.

Megilah 28a: One of the merits to which R. Nechunya ben Hakanah attributed his long life was that he did not sleep before forgiving one who had cursed him.

This is like Mar Zutra, who would forgive all who wronged him before going to sleep.

Bava Kama 92a - Mishnah: Even though the damager pays the victim, he must ask the victim for forgiveness. If the victim does not forgive, he is cruel - "Avraham prayed...and Hash-m cured Avimelech".

Rishonim

Rambam (Hilchos De'os 7:7,8): One who takes vengeance transgresses the Lav of Lo Sikum. Even though he is not lashed, it is a very bad attitude. Rather, a person should overlook all worldly matters (in which he was wronged). People of understanding know that such matters are folly and not worth avenging.

Similarly, one who bears a grudge transgresses the Lav of Lo Situr. As long as he bears resentment he is prone to take vengeance. Rather, he must erase the matter from his heart; this is the proper Midah that enables settlement of the world and interpersonal relations.

Question: Why did the Bas Kol say that R. Akiva is not greater? He was greater in the Midah of Ma'avir Al Midosav!

Answer (Or Yisrael 28): R. Eliezer was a Talmid of Beis Shamai. He held that the Halachah requires one to be a Kapdan (exacting) regarding matters of Kavod ha'Torah, like Shamai. He acted exactly as he should have. R. Akiva was a Talmid of Beis Hillel. Hillel held that one should always act with humility. Even though both acted according to what they believed to be the Halachah; there was a special reward to R. Akiva for being Ma'avir Al Midosav. Nowadays, after the Halachah was fixed like Beis Hillel, it is a great sin to be a Kapdan like Shamai.

Rambam (Hilchos Teshuvah 2:10): It is forbidden to be cruel and to refuse to be appeased. Rather, one must be easy to appease and difficult to anger. When the sinner asks forgiveness, the hurt party should forgive with all his heart and desire. Even if the person sinned greatly, the victim should not bear a grudge or take vengeance.

Sha'arei Teshuvah (1:28): A Ba'al Teshuvah should be humble in front of everyone. This will cause that he not get angry or irritated at people, and to ignore (insulting) things that he hears. Being Ma'avir Al Midosav atones for sins. A person is forgiven for everything, Midah k'Neged Midah. This is a very dear opportunity.

Sefer ha'Chinuch (Mitzvah 241): One may not take vengeance against a Yisrael for any harm or pain. Most people seek to return the harm or hurt they suffered at the hands of others. "Lo Sikum" forbids this. One must put to his heart that everything that happens to him is from Hash-m; all suffering was decreed because of his sins. When Shim'i ben Gera cursed David, David said 'Let him curse - Hash-m told him to!' One who decides to hate someone because he did evil to him transgresses this Lav. One is not lashed for it because one can transgress without an action.

Be'er Mayim Chayim (introduction to Chafetz Chaim, Lavim 8-9): Sefer ha'Chinuch forbids avenging or bearing a grudge after one was insulted. However, the Chinuch himself (Mitzvah 338) says 'one is not commanded o be silent to one who insults him. It is impossible for a person to be like a rock; further, this would be like admission to the insults.' One may retaliate at the time he is insulted; it is a praiseworthy Midah not to.

Poskim

Shulchan Aruch (OC 606:1): If Reuven sinned against Shimon, even through words, Yom Kipur does not atone for him unless he appeases Shimon.

Kaf ha'Chayim (13,14): Shimon should present himself to give Reuven opportunity to ask forgiveness (Yoma 87a). If one does not remove hatred from his heart on Yom Kipur, his prayer is not heard.

Rema: Shimon should not be cruel and refuse to forgive.

Source (Gra DH veha'Mochel): We learn from Bava Kama 92a and the episode with R. Chanina (the Gemara asked why he did not forgive, and explained his reason for this).

Mishnah Berurah (8): If one refuses to forgive, Hash-m will refuse to forgive him. If one pardons Mezid transgressions, Hash-m will do likewise to him (Sha'ar ha'Tziyon 8).

Kaf ha'Chayim (43,44,45): It is good for the Shali'ach Tzibur to ask everyone to forgive each other before Kol Nidrei. In any case everyone should say that he forgives all who sinned against him in any way. A parent should say that he totally forgives his child, even if the child did not request. A husband should forgive his wife for spending money against his wishes.

Rema: He may refuse to forgive if he intends for Reuven's good.

Source #1 (Bach DH v'Da): Presumably, the Rema explains that R. Chanina intended for Rav's good, lest Rav become Rosh Yeshiva and the yoke of the Tzibur would cause Rav to lose time from learning. It is not clear why the Rema explains unlike Rashi (that R. Chanina intended for his own benefit).

Note: R. Chanina knew that if Rav goes to Bavel Rav will be Rosh Yeshiva there. Either way, he will lose time from learning! Perhaps R. Chanina knew that (at the time) there were much fewer Talmidim in Bavel and they would impose a smaller demand on Rav's time than Talmidei Eretz Yisrael. Perhaps R. Chanina interpreted the Hashgachah. Special circumstances led Rav to offend R. Chanina, and R. Chanina had the dream. He understood that Hash-m wanted Rav to go to Bavel to establish Yeshivos there (see Rashi Gitin 6a DH mi'Ki).

Source #2 (Taz 2): The Rema explains like Rashi; R. Chanina intended for his own benefit. The Rema holds that similarly, one may refuse to forgive for the benefit of the sinner.

Mishnah Berurah (9): Even in such a case Shimon must remove hatred from his heart because Reuven requested forgiveness.

Rema: One need not forgive one who was Motzi Shem Ra.

Source (Gra DH v'Im): The Yerushalmi says that there is no forgiveness for Motzi Shem Ra.

Magen Avraham (5): He need not forgive because people who heard the Shem Ra might not hear the appeasement. Nevertheless, it is praiseworthy to forgive even this.

Kaf ha'Chayim (33): Pesach Einayim says that even for Motzi Shem Ra it suffices to ask forgiveness three times. Lev David says that there is no forgiveness until the person is appeased.