Riyad Us-Saliheen (Gardens of the Righteous)

Chapter 133
Etiquette of offering Greetings

857. Abu Hurairah (May Allah be pleased with him) reported: Messenger of Allah (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).''
[Al-Bukhari and Muslim].

   The narration in Al-Bukhari adds: Messenger of Allah (PBUH) said, "The young should greet the elderly.''

Commentary: The greeting of As-Salamu Alaikum should be uttered according to the prescribed way. It is the situations under reference and not the grades which will be taken into consideration in this respect.

858. Abu Umamah Sudaiy bin `Ajlan Al-Bahili (May Allah be pleased with him) reported: The Messenger of Allah (PBUH) said, "The person nearest to Allah is one who is the first to offer greeting.''
[Abu Dawud].

The narration in At-Tirmidhi is: The Messenger of Allah (PBUH) was asked: "O Messenger of Allah! When two persons meet, who should greet the other first?'' The Messenger of Allah (PBUH) said, "The person nearest to Allah (i.e., one who is more obedient and therefore closer to Allah will say: As-Salam first.''

Commentary:  The degree of a man's humbleness and modesty will be measured by the degree of his nearness to Allah. One who is nearer to Allah is always the first to offer As-Salam to others, while others stick to their stuck-up behaviour