His 2005 book No god but God: The Origins, Evolution, and Future of Islam tells the story of Islam carefully, lucidly and with warm affection for his faith's core.
Explaining Islam to western Christians requires historical narrative. After all, for Muslims, God's revelation through the Prophet Muhammed happened in known locales (trading centers on the Arabian Peninsula) at known dates (between 610 and 622 C.E.) and led to material consequences that are fully documented (one of the worlds great empires extending from Spain to the Hindu Kush). The Muslim story makes the tales of that Jewish Galilean carpenter's perambulations around ancient Palestine seem vague, mythological, in the modern pejorative sense.
Aslan is an Iranian-American, a refugee from his native country's harsh theocracy; in this book he is exploring whether his faith can be compatible with the contemporary wider world. He makes a strong case that the history of Islam contains episodes of great openness to diversity, as well as a core commitment in establishing justice and equality among people. But whether Muslim peoples can find their way to Islamic democracies remains hard for him to envision. Here's a sample of this sort of wrestling with possibilities not yet born:
I've read quite a few accounts of the history and beliefs of the Islamic faith. When Muslims get to hoping for a Reformation -- a struggle within the faith to both preserve and accommodate its core within a contemporary context -- I feel like I'm being a Peeping Tom. This is up the believers, not outsiders. But we live in a world where outsiders can and will see in; a Muslim Reformation, if one is accomplished, will happen in full view of all others. Given this reality, I can heartily recommend Aslan's depiction of Islam to others peering in the global window.