You've read the proof-texts. You've seen how violent and intolerant the Qur'an can seem, when choice words are lifted off the page by atheists, Christians and Jews who wish to paint Islam as inherently violent and intolerant. Of course, these same Christians and Jews will object strenuously when their own scriptures are quoted back at them. "No. That verse has to be read in light of this verse." "You're taking that out of context. You have to understand the history of the time." (And so on.) Here is a sampling of passages from the Qur'an which show that there is more to the story that Islam's accusers are telling:
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We [i.e., God] have assigned a law and a path to each of you [Muslims, Jews, and Christians]. If God had so willed, He would have made you one community, but He wanted to test you through that which He has given you, so race to do good: you will all return to God and He will make clear to you the matters you differed about. (5:48)
Believers, argue only in the best way with the People of the Book [Jews and Christians], except with those of them who act unjustly. Say, “We believe in what was revealed to us and in what was revealed to you; our God and your God are one [and the same]; we are devoted to Him.” (29:46-47) [The surah goes on to state that those who disbelieve will be judged by God at the appointed time; the point here is that Muslims are not to take it upon themselves to punish unbelievers.]
But they are not all alike. There are some among the People of the Book who are upright, who recite God’s revelations during the night, who bow down in worship, who believe in God and the Last Day, who order what is right and forbid what is wrong, who are quick to do good deeds. These people are among the righteous and they will not be denied [the reward] for whatever good deeds they do: God knows exactly who is conscious of Him. (3:113-115)
Some of the People of the Book believe in God, in what has been sent down to you and in what was sent down to them: humbling themselves before God, they would never sell God’s revelation for a small price. These people will have their rewards with their Lord: God is swift in reckoning. (3:199)
The [Muslim] believers, the Jews, the Christians, and the Sabians—all those who believe in God and the Last Day and do good—will have their reward with their Lord. No fear for them, nor will they grieve. (2:62)
For the [Muslim] believers, the Jews, the Sabians, and the Christians—those who believe in God and the Last Day and do good deeds—there is no fear: they will not grieve. (5:69)
Say, “People of the Book, let us arrive at a statement that is common to us all: we worship God alone, we ascribe no partner to Him, and none of us takes others beside God as lords.” If they turn away, say, “Witness our devotion to Him.” (3:64)
Prophet, tell them [the People of the Book], “All grace is in God’s hands: He grants it to whomever He will—He is all embracing, all knowing—and He singles out for His mercy whomever He will. His grace is infinite.” (3:73-74)
There is no compulsion in religion: true guidance has become distinct from error, so whoever rejects false gods and believes in God has grasped the firmest hand-hold, one that will never break. God is all hearing and all knowing. (2:256)
Say, “Now the truth has come from your Lord: let those who wish to believe in it do so, and let those who wish to reject it do so.” (18:29)
Had your Lord willed, all the people on earth would have believed. So can you, Prophet, compel people to believe? No soul can believe except by God’s will, and He brings disgrace on those who do not use their reason. (10:99-100)
Say to the disbelievers, “I do not worship what you worship, and you do not worship what I worship. I will never worship what you worship, and you will never worship what I worship. You have your religion, and I have mine.” (109:1-6)
Hurry towards your Lord’s forgiveness and a Garden as wide as the heavens and earth prepared for the righteous, who give, both in prosperity and adversity, who restrain their anger and pardon people—God loves those who do good—those who remember God and implore forgiveness for their sins if they do something shameful or wrong themselves—who forgives sins but God?—and who never knowingly persist in doing wrong. The reward for such people is forgiveness from their Lord, and Gardens graced with flowing streams, where they will remain. How excellent is the reward of those who labor! (3:133-136)
On account of [Cain’s deed], We [God] decreed to the Children of Israel that if anyone kills a person—unless in retribution for murder or spreading corruption in the land—it is as if he kills all mankind, while if any saves a life it is as if he saves the lives of all mankind. (5:32)
Fight in God’s cause against those who fight you, but do not overstep the limits [according to the commentators this means: do not initiate hostilities, do not kill non-combatants, and do not give disproportionate response to aggression]: God does not love those who overstep the limits. . . . If they cease [hostilities], then God is most forgiving and merciful. . . . If they cease hostilities, there can be no further hostility, except towards aggressors. . . . Spend in God’s cause: do not contribute to your destruction with your own hands, but do good, for God loves those who do good. (2:190-195)
But if they incline towards peace, you must also incline towards it, and put your trust in God: He is the All Hearing, the All Knowing. (8:61)
If you raise your hand to kill me, I will not raise mine to kill you. I fear God, the Lord of all worlds. (5:28)
God may still bring about affection between you and your present enemies—God is all powerful, God is most forgiving and merciful—and He does not forbid you to deal kindly and justly with anyone who has not fought you for your faith or driven you out of your homes: God loves the just. (60:7-8)
The Prophet said, “When God had finished His creation, He wrote over His throne: ‘My Mercy preceded My Anger.’” (Sahih Bukhari ix, 93:518)
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Read the Qur'an. I recommend this translation. Read John Esposito's What Everyone Needs To Know About Islam. Read Karen Armstrong's Muhammad: A Prophet for Our Time. Better yet, go to your local mosque and tell them you want to get to know the people there and learn to understand their religion. Spend two or three months, at least, visiting and discussing, asking questions, and listening. Drop your defenses. Make friends. Put an end to ignorance, fear, and hate. Do unto others as you would have them do unto you.