Muslims have an obligation towards one another to offer greetings when they meet. The fulfillment of this social responsibility not only creates a sense of cohesion and feelings of respect for one another but also have great rewards.  “As-Salamu Alaikum wa Rahmatullahi wa Barakatuhu” - Translation: May you be safe from evil, and the Mercy of Allah and His Blessings be upon you.

AllahSWT says in the holy Quran: “O you who believe! Enter not houses other than your own, until you have asked permission and greeted those in them'' (24:27)… “But when you enter the houses, greet one another with a greeting from Allah, blessed and good'' (24:61). 

A man asked the Prophet PBUH, "Which act in Islam is the best?''  He PBUH replied, "To feed people, and to greet everyone (Muslims), whether you know or you do not”. [Bukhari & Muslim]

Prophet PBUH said, “When you enter your house, say “As-Salamu Alaikum”  to your family, for it will be a blessing both to you and to your family.''

Prophet PBUH said, “A rider should greet a pedestrian; a pedestrian should greet one who is sitting; and a small group should greet a large group (of people)”. In another narration it is mentioned, “The young should greet the elderly''. [Bukhari & Muslim]

Anas (R.A) passed by some children and greeted them. Then he said: "Messenger of Allah PBUH used to do the same.'' [Bukhari & Muslim]

Prophet PBUH said, "The person nearest to Allah is one who is the first to offer greeting''.  [Abu Dawud]

The Messenger of Allah PBUH commanded us to do seven things: 1) to visit the sick  2) To follow the funeral of a dead believer  3) To invoke the Mercy of Allah upon one who sneezes (saying to him/her Yarhamuk-Allah)  4) To support the weak  5) To help the oppressed  6) To promote the greeting of “As-Salamu Alaikum”   7) To help those who swear to do something to keep their oaths. [Bukhari & Muslim].