Relationship with non Muslims in islam

As Muslims living in the West, we interact with non-Muslims on a daily basis whether at work, university, college, school or in society at large. It is incorrect for us to cut ourselves completely from them and live in isolation. We should aim at building relationships with them in order to give them da'wah to embrace Islam. It is important to always remind ourselves that our purpose in this life is to carry Islam to everybody and show them the right path - to rid themselves of the misery of man-made systems, thereby achieving the pleasure of Allah سبحانه وتعالى. We have to be aware of our purpose in this life and what may influence our adherence to Islam. Friendship plays a major influence in our lives, and so choosing good friends is not a trivial matter. Allah سبحانه وتعالى revealed, 
يَا أَيُّهَا الَّذِينَ آمَنُواْ لاَ تَتَّخِذُواْ بِطَانَةً مِّن دُونِكُمْ لاَ يَأْلُونَكُمْ خَبَالاً وَدُّواْ مَا عَنِتُّمْ قَدْ بَدَتِ الْبَغْضَاء مِنْ أَفْوَاهِهِمْ وَمَا تُخْفِي صُدُورُهُمْ أَكْبَرُ قَدْ بَيَّنَّا لَكُمُ الآيَاتِ إِن كُنتُمْ تَعْقِلُونَ 
"O you who believe! Do not take for intimate friends from among others than your own people; they do not fall short of inflicting loss upon you; they love what distresses you; vehement hatred has already appeared from out of their mouths, and what their breasts conceal is greater still; indeed, We have made the communications clear to you, if you will understand." [Al-Imran, 3:118] 
Weakness is part of human nature and being surrounded by friends who have no ties to the values of Islam is a slippery slope with one known outcome - slipping away form the right path and losing one's Deen. The pressure from the circle of friends is far stronger than the pressure from family. Without strong understanding of the values of Islam and a constant reminder from our friends, our youth will find themselves forced to "blend in". Such a Muslim would find himself in a situation wherein he/she is willing to hide his/her Islam in front of those who despise it (those that he/she considers as friends) and to separate from the believers. When this situation occurs, a point is reached when there is little difference between the Muslim and his wrong-doing companion. Such a companionship is one of the causes of sickness of one's heart and loss of one's Deen. 
Instead of making friends with the misguided people we should befriend the righteous and treat the rest in a gracious and just manner. Staying at a sufficient distance is necessary; yet treating everybody in a noble and kind manner is also required. So let us take heed before the inevitable Day when we are called to account for our actions. Allah سبحانه وتعالى says: 
الْأَخِلَّاء يَوْمَئِذٍ بَعْضُهُمْ لِبَعْضٍ عَدُوٌّ إِلَّا الْمُتَّقِينَ 
"Friends on that Day will be enemies one to another, except al-Muttaqoon (i.e. those who have Taqwah)." [Az-Zukhruf, 43:67]