The Rules of Greeting One Another

Ayatullah al-`Uzma al-Hajj ash-Shaykh Lutfullah as-Safi al-Gulpaygani
Issue 454: It is Mustahab to greet one another, but it is Wajib to reply the greeting.
Issue 455: It is Makruh to greet someone who is praying Salat.
Issue 456: If someone says Salam to one who is praying Salat, then the reply must be given exactly as it originally was worded; for example, if it is said: “سَلامُ عَلَيْكُمٌ” then the reply must be given as: “سَلامُ عَلَيْكُمٌ”, but if the greeting is: “عَلَيْكُمُ السَّلامُ”, then according to Ihtiyat Wajib, the reply must be given as: “سَلامُ عَلَيْكُمٌ.”
Issue 457: It is not permissable for one who is reciting the Salat to say Salam to another person (to initiate it).
Issue 458: The reply to a Salam must be given immediately.
Issue 459: If two people say Salam to each other at the same time, then it is Wajib that both of them reply to the Salam of the other person.
Issue 460: Saying Salam to a non-Muslim is Makruh, but if the non-Muslim says Salam to a Muslim, then according to Ihtiyat Wajib, the reply must be given as “عَلَيْكُمٌ” or one must only say “سَلامٌ.”

Etiquette’s of Greeting One Another
Issue 461: It is Mustahab that the one who is riding greet the one who is walking, and that the one who is standing greet the one who is sitting, and that a small group of people greet the large group of people, and that the younger one greet the older one.
Issue 462: It is Mustahab - except in Salat - to reply the Salam in a better manner; therefore, if someone says to you: “سَلامُ عَلَيْكُمٌ” it is Mustahab to reply by saying: “ سَلامُ عَلَيْكُمٌ وَ رَحْمَةُ اللهِ.”
Issue 463: It is Makruh for a man to say Salam to a woman, especially if it is a young woman.