Gemara

15a: She'alas Shalom is forbidden to an Avel, for Hash-m told Yechezkeil "He'anek Dom".

21b (Beraisa): Greeting with 'Shalom' is forbidden to an Avel the first three days. From the third day until the seventh he answers Shalom, but does not greet. After this, he may greet and answer normally.

Contradiction (against the Reisha - Beraisa): A case occurred, and R. Akiva's children died. All of Yisrael entered and gave a great eulogy. When they were leaving, R. Akiva stood on a big bench and praised them. He blessed them with Shalom.

Resolution: Showing honor to the Rabim is different.

Contradiction (against the Seifa - Beraisa #1): If one encounters his friend, an Avel within 30 days, he consoles him but does not give Shalom. If it is after 30 days, he gives Shalom but does not console him. If Reuven's wife died and he remarried, one may not enter Reuven's house to console him. If one found Reuven in the market, he consoles in a soft, serious voice.

Answer (Rav Idi bar Avin): The Avel may give Shalom (after seven days), because others are amidst Shalom. Others may not give Shalom to the Avel, because he is not amidst Shalom.

Question: The Beraisa says that he answers Shalom. This connotes that others may greet him with Shalom!

Answer: It discusses people who did not know (that he is an Avel).

Question: If so, the same applies even in the first three days!

Answer: In the first three days he informs them that he is an Avel but does not return Shalom. After this, he may answer without informing them.

Contradiction (Beraisa #2): If one encounters his friend, an Avel within 12 months, he consoles him but does not give Shalom. If it is after 12 months, he gives Shalom but does not console him; he speaks with him indirectly ('you should be consoled', without mentioning the Mes);

R. Meir says, if one encounters his friend, an Avel after 12 months, and consoles him, this is like a man who broke his leg, and it healed. A doctor told him 'come to me. I will break your leg and heal it, so you will know that my medicines are good.'

Resolution: Beraisa #2 discusses one who lost a parent. Beraisa #1 discusses one who lost another relative.

Question: Also regarding other relatives, he should console indirectly!

Answer: Indeed, Beraisa #1 means that after 30 days one does not console him normally, but he consoles indirectly.

26b - Rav Papa - Beraisa: An Avel should not hold a young child in his lap lest this bring him to laugh, and people will despise him.

Rishonim

Rif and Rosh (3:38): Greeting with 'Shalom' is forbidden to an Avel the first three days. If people did not know that he is an Avel and gave Shalom to him, he informs them that he is an Avel but does not return Shalom. If this happened from day three until day seven, he may answer without informing them. From day seven until day 30 he may give Shalom to others, for they are amidst Shalom. Others may not give Shalom to him until after 30 days. This refers to one who lost other relatives. If one lost a parent, they do not give Shalom to him within 12 months.

Nimukei Yosef (DH b'She'alas): The Isur of She'alas Shalom includes greeting and answering. However, if many people honored the Avel he may give to them Shalom, like R. Akiva did.

Nimukei Yosef (DH uvi'Gmara): It seems that if one encounters an Avel within 30 days and did not yet console him, he says 'Hashem should console you from this mourning.' If it is after 12 months, he says just 'Hashem should console you.'

Rambam (Hilchos Evel 5:20): We learn that She'alas Shalom is forbidden to an Avel from "He'anek Dom". The first three days if someone and gave Shalom to him, he informs them that he is an Avel but does not return Shalom. From day three until day seven, he returns Shalom. From day seven until day 30 he may give Shalom to others, but they may not give Shalom to him until after 30 days. If one lost a parent, people do not give Shalom to him until after 12 months. Since She'alas Shalom is forbidden, all the more so he may not talk much and be frivolous, for it says "Dom". He should not hold a young child in his lap lest this bring him to laugh. He should not enter a place of Simchah such as a tavern.

Kesef Mishneh: The Rambam himself made the Isurim of excessive talk, frivolity and entering a place of Simchah. These are proper.

Rambam (10:1): An Avel does not publicly mourn on Shabbos. He gives Shalom to everyone on Shabbos.

Rosh (ibid.): The Yerushalmi permits to give Shalom to Avelim on Shabbos where this is the custom. It is the custom in the south. If one encounters his friend, an Avel within 30 days, he consoles him but does not give Shalom. If it is after 30 days, he gives Shalom but does not console him directly. He speaks with him indirectly. If Reuven's wife died and he remarried, one may not enter Reuven's house or console him. If one found Reuven in the market, he consoles in a soft, serious voice. If one lost a parent, within 12 months one consoles him but does not give Shalom. After 12 months he not console him; he speaks with him indirectly. Consoling an Avel after 12 months is like a doctor telling one (whose broken leg healed) '...I will break your leg and heal it...'

Poskim

Shulchan Aruch (YD 385:1): Greeting with 'Shalom' is forbidden to an Avel. The first three days he does not give Shalom to anyone. If people did not know that he is an Avel and gave Shalom to him, he informs them that he is an Avel but does not return Shalom. From day three until day seven he does not greet. If people did not know that he is an Avel and gave Shalom to him, he answers. From day seven until day 30 he may give Shalom to others, for they are amidst Shalom; all the more so he may return Shalom. Others may not give Shalom to him.

Beis Yosef (DH Kosvu): Hagahos Maimon says that if Mes died a day before Rosh Hashanah, one does not give Shalom to the Avel until two days after Yom Kipur.

Bach (340 DH Kosav bi'Tshuvas Maimoni): Regarding She'alas Shalom, Yom Tov does not Mevatel the period of 30 days.

Note: The Tur (399) explains that Rosh Hashanah ends Shiv'ah. Rosh Hashanah and Yom Kipur each counts like seven days towards the remaining 23.

Shulchan Aruch (ibid.): After 30 days he is like a regular person. This refers to one who lost other relatives. If one lost a parent, he may give Shalom after seven days, but others may not give Shalom to him until after 12 months.

Rema: Since She'alas Shalom is forbidden, all the more so he may not talk much. He may give Shalom to the Rabim to honor them, e.g. if they came to console him. Nowadays some are lenient about giving Shalom after 30 days. There is no reason for this, unless they will say that the way we greet today is not what the Gemara calls She'alas Shalom.

Shach (2): This is not a good reason, for if so it should be permitted even within 30 days.

Shulchan Aruch (2): If one encounters his friend, an Avel within 30 days, he consoles him but does not give Shalom. If it is after 30 days, he gives Shalom but does not console him directly, rather, indirectly. He does not mention the name of the Mes; he just says 'you should be consoled'. If Reuven's wife died and he remarried, one may not enter Reuven's house to console him. If one found Reuven in the market, he consoles in a soft, serious voice. If he did not remarry, one consoles him until three festivals pass. If one lost a parent, within 12 months one consoles him. After 12 months he speaks with him indirectly.

Shulchan Aruch (3): We give Shalom to Avelim on Shabbos where this is the custom. The Rambam says that an Avel gives Shalom to everyone on Shabbos, for this is like public matters.

Rema: One may not send gifts to an Avel within 12 months of losing a parent. On Shabbos it is permitted only in a place where we give Shalom to Avelim on Shabbos.