Greeting each other

Narrated Abu Huraira:

Allah's Apostle (may peace be upon him) said, "The riding person should greet the walking one, and the walking one should greet the sitting one, and the small number of persons should greet the large number of persons."

Narrated Abu Huraira: Allah's Apostle (may peace be upon him) said, "The younger person should greet the older one, and the walking person should greet the sitting one, and the small number of persons should greet the large number of persons."

[Sahih Al Bukhari : book 74, hadith 252]

Narrated 'Abdullah bin 'Amr:

A man asked the Prophet , "What sort of deeds or (what qualities of) Islam are good?" The Prophet replied, 'To feed (the poor) and greet those whom you know and those whom you do not Know.

[Sahih Al Bukhari : book 2, hadith 27]

Greeting each other with "Asalaam Alaikum" and responding back with " Walaikum Asalaam" is considered as one of the good deeds of Islam for a Muslim.
The hadith explains who should take the initiative to greet in different situations, remember the first one to greet gets more rewards.

Asalaam Alaikum :-)