The Etiquette & Rules  of Greeting / Salam

Quran 4 :86 And when you are greeted with a greeting, greet with a better (greeting) than it or return it; surely Allah takes account of all things. 

Greeting with Peace ( salam) is a voluntary act whereas returning it is an obligation- Holy Prophet -Kanzul amal no25294

The Prophet (saws) said :-

The young should greet the old

A single individual should greet two together

The fewer number should greet the larger number

The person on horseback should greet the person on foot

The person walking should greet the one standing

The person standing should greet the one sitting

-Source Mizan ul Hikmah kanzul amal no25321

The Prophet saws said -There are 5 things I will never leave until death...and greeting the young in order that it may remain a practice after me -bihar v76 p10 no 38

Imam Baqir (as) said- Do not extend greeting of peace... and to those who drink alcohol ,nor to chess & dice players, nor to an effeminate person ,nor to someone performing his prayer ( because he cannot return the greeting) bihar v76 p9no 35

  Rules of Salam & Its reply

-It is mustahab to say salām, but wajib to REPLY, IMMEDIATELY to salam, even if one is reciting salat, such that he who said salam hears it.

-It is wajib to reply to the salam of a child. It is also wajib to reply to the salam of a person who is not mahram to you.

-If someone says salam to a group of people, it is wajib upon all to reply & if any 1 of them replies, it is now mustahab for the rest to reply

-If two people together say salaam to each other: each of them must reply to the salaam of the other.

-If a person says salam more than once, it is enough to reply once. If he says salam again after you have replied: it is wajib to reply again

-It is not wajib to reply to salam in text messages, watsapp, emails etc.

-It is not wajib to reply to a salām that is said mockingly or jokingly.

-If a person says salam to a group of people & a person, not from this group, replies: it remains wajib upon the group to reply.

-It is recommended that a person who is standing should say it to one who is sitting, and the younger of two people should say it to the older person.

- it is mustahab (except in prayers), that the reply to salām should be better than the salām itself. For example, if one says ‘salāmun ‘alaykum’, the reply be ‘salāmun ‘alaykum wa rahmatul lāh’.

-If a person intentionally or due to forgetfulness delays his reply to salām to the extent that were he to reply to it, it would not be considered a reply to that initial salām, then, in the event that he is performing prayers he must not reply, and if he is not performing prayers then replying is not obligatory.

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-It is makrooh to say salam to one who is reciting salat

- If someone says salam to a group of people, one of whom is reciting salat:if someone else replies to the salam, the salat reciter must not reply

-If one says salam to a group of people one of whom is reciting salat: if the salat reciter doubts that he was addressed , he must not reply.?

-If someone says salam to a group of people, one of whom is reciting salat: if the salat reciter doubts that the reply was given, he should reply.

-If a person who is performing prayers does not reply to a salām, then even though he commits a sin his salat is valid.

http://islamic-laws.com/tawzeh/119.html

1146. A person offering prayers should not greet anyone with Salam, and if another person says Salam to him, he should use the same words in reply without adding anything to it. 
For example, if someone says Salamun alaykum, he should also say Salamun 'alaykum in reply, without adding Wa rahmatullahi wa barakatuh. As an obligatory precaution, he should not utter 'Alaykum' or 'Alayka' before the word Salamun if the one who greeted him did not say so. In fact, the recommended precaution is that the reciprocation must fully conform with the way Salam was initiated. 
So if he said: Salamun alaykum, the reply should be Salamun alaykum, and if he said: As-Salamu alaykum, then the reply should be the same. Similarly, the reply to Salamum alayka will be Salamun alayka. But if someone initiated Salam saying Alaykumus Salam, then the answer can be given in any of the phrases.

1147. It is necessary that the reply to Salam is given at once, irrespective of whether one is praying or not. And if, whether intentionally or due to forgetfulness, he delays reply to the Salam, so much that if he gives a reply after the delay, it may not be reckoned to be a reply to that Salam, then he should not reply if he is in namaz. And if he is not in namaz it is not obligatory for him to reply.

1148. A person should reply to a Salam in a way that one who greets him can hear it. However, if he who says salam is deaf, or passes away quickly, then it is necessary to make reciprocation by sign etc., if that would be understood. If that is not possible, then it is not obligatory to respond when one is not praying. And if one is praying, it is not permissible.

1149. It is obligatory that a person who is in namaz, responds to Salam with the intention of greeting. But if he responds with the intention of prayers or blessing, meaning "May Allah bless You", there is no harm.

1150. If a woman or a Na-Mehram or a discerning child, that is, one who can distinguish between good and evil, says Salam to a person in namaz, the person should respond. However, in reply to the Salam by a woman who says Salamun alayka, the person offering prayers can say Salamun alayki, giving Kasrah to Kaf at the end.

1151. If a person in namaz does not respond to Salam, his prayers are in order, though he will have committed a sin.

1152. If a person says Salam to a person in namaz in a mistaken way, such that it cannot be treated as a Salam, it is not permissible to reply to it.

1153. It is not obligatory to give reply to the Salam said in jest, or the Salam of a non-Muslim man or woman who is not a Zimmi (an infidel living under the protection of an Islamic Government). And if he/she is a zimmi, it is sufficient, on the basis of obligatory precaution, to answer saying 'alayka' only.

1154. If a person says Salam to a group of people, it is obligatory for all of them to give a reply. However, if one of them replies, it is sufficient.

1155. If a person says Salam to a group of people, but a person for whom it was not intended gives a reply, it will still be obligatory upon the group to reply.

1156. If a person says Salam to a group among whom one was in namaz, and that person doubts whether Salam was intended for him or not, it will not be necessary for him to give a reply. And if the person offering prayers is sure that he was also intended by the one who greeted, but some one else has made a response, he does not have to reply. But if he is sure that he was among the group for whom Salam was intended, and no one has replied, then he should reply.

1157. It is Mustahab to greet with Salam, and it has been emphatically enjoined that a person who is riding should greet one who is walking, and a person who is standing should greet one who is sitting, and a younger person should greet an elder.

1158. If two persons simultaneously say Salam to each other, each one of them should, on the basis of obligatory precaution, reply the Salam of the other.

1159. When a person is not in namaz, it is Mustahab that his response to the Salam should be more expansive. For example, when one says salamun alaykum, the other should say salamun alaykum wa rahmatullah in reply.