Wishing peace is the way of greeting in Islam
The Muslims when they meet and part with each other say Assalam-o-Alaikum. It means peace be upon you. Consider the following two verses of Quran about the greetings of peace.

"Salâmun 'Alaikum (peace be upon you) for that you persevered in patience! Excellent indeed is the final home!" QuranAr-Rad [13:24]

And verily, there came Our Messengers to Ibrahim (Abraham) with glad tidings. They said: Salam (greetings or peace!) He answered, Salam (greetings or peace!) and he hastened to entertain them with a roasted calf. Quran Hud [11:69]

Peace is the ultimate reward in the hereafter
Allah Almighty has made heaven a home of the peace. In the first verse of online quran academy given below, it is explicitly mentioned that the people who do good deeds will be rewarded with peace. In the second verse given below Allah Almighty calls the heaven a home of peace!

"(It will be said to them): 'Enter therein (Paradise), in peace and security.' Quran Al-Hijr [15:46]

Allah calls to the Home of peace (i.e. Paradise, by accepting Allah's religion of Islamic Monotheism and by doing righteous good deeds and abstaining from polytheism and evil deeds) and guides whom He wills to a Straight Path. Quran Yunus [10:25]

Prophet Ibrahim (A.S) prayed for peace
All the Muslims know that Makkah is the city of peace. Few people know about the prayer of prophet Ibrahim (A.s) in this regard.

And (remember) when Ibrahim (Abraham) said: "O my Lord! Make this city (Makkah) one of peace and security, and keep me and my sons away from worshipping idols. Quran Ibrahim [14:35]

Prophet Noah (A.S) was also rewarded peace
The reward for Prophet Noah (A.S) was also peace.

It was said: "O Nûh (Noah)! Come down (from the ship) with peace from Us and blessings on you and on the people who are with you (and on some of their off spring), but (there will be other) people to whom We shall grant their pleasures (for a time), but in the end a painful torment will reach them from Us." Quran Hud [11:48]

Allah Almighty appreciates the one who strives to make peace
Some people say that Islam promotes violence. However if they read the three verses of the Quran given below, their perception might be changed.