I am by no means an interfaith expert, so please take this syllabus in the spirit it is offered, as a starting point, suggestions from a Christian blogger on a starting point in order to understand our faith in relationship to Islam better.
First, watch Of Gods and Men. Then watch it again. Then watch it again.
Next, read A Common Word.
For excellent tools to overcome blatant Islamophobia, read:
For the great and classic text that will change your life:
For an argument that Christians and Muslims worship the same God, from one of our greatest living theologians:
And a similar expression of faith from a Muslim scholar:
Finally, a recent and accessible study Qur'an: