Yes! It's not exactly like biblical criticism, though, since the two texts are so different. The Bible is a compilation of texts, each written in its own time and place, sometimes centuries apart. The Qur'an, by comparison, purports to be words spoken by God, transmitted to Muhammad, and then written down shortly thereafter. This means that many of the tools and methods used by biblical scholars aren't always appropriate for Quranic studies.

In particular, biblical criticism often focuses on recovering the authorial text, that is, the text of a particular book in the Bible as it was originally written. Sometimes, this means discerning underlying sources or influences that were sort of intermediary reports between actual events and the books that we now have. For example, it seems like the authors of Matthew and Luke each had a handbook of sayings attributed to Jesus (called Q for Quelle, the German word for 'source'), and they incorporated these sayings into their gospel accounts at different points. By sifting out the sayings of Jesus that appear in different contexts in both gospels, scholars think they've come up with a pretty good reconstruction of what Q looked like, even though no copies of this text survive—if indeed it was ever written down and not just a list of quotes that early Christians memorized. Similarly, by hunting down inconsistencies within a single book, such as the multiple forms of identifying God used in the Book of Genesis, biblical scholars have deduced multiple sources that were later compiled into one.

Although some scholars have tried to apply similar methods to the Qur'an, I don't think they've been effective. From a methodological standpoint, they don't have other texts they can compare it to, like they do with the four multiple gospel accounts. Moreover, no book in the bible claims that God was the author, so there's no problem trying to unpack out how the authors wrote their texts. On the other hand, if we accept that God really could be the author behind the Qur'an, these questions are moot. So this method doesn't work. The Qur'an is not clearly derivative from any previous source, and even when there are references to other sources (such as the Five Sleepers, or the Alexander legends), they don't show plagiarism or influence but rather God speaking in an idiom that seventh-century Arabs would be able to understand. And if there are stylistic inconsistencies within the Qur'an, they can easily be attributed to the fact that these verses were revealed at different times during the course of Muhammad's career and address the different concerns that his community was facing. So while some scholars have used the tools of biblical criticism to debunk Islam as a man-made myth, both the text and the theology of the Qur'an have made their own work bunk.

The other major tool of biblical criticism is manuscript analysis. Basically, this means looking at a large number of old copies of biblical manuscripts, trying to deduce how errors crept in, and then figuring out what the text would look like if we removed those errors. Jerome supposedly did this back around 400 when he published an authorized translation of the bible into the common language of the time, Latin (i.e. the Vulgate). This later became a major catalyst for the field of philology, especially in Germany in the 1800s, where some astoundingly brilliant scholars bent their wills toward reconstructing the Bible as it was originally written. By getting closer to the original text, German Protestants argued, they could cut out the middle man of the Roman Catholic Church and start interpreting the Bible themselves. More recently, Bart Ehrman has revived popular interest in manuscript studies through his provocatively titled Misquoting Jesus (2005). Ehrman is a serious scholar who provides a very accessible introduction to biblical criticism and shows how early Christians edited manuscripts of the bible to adapt them to the theological disputes of their day. For Ehrman, this undermined his personal faith, and his skepticism occasionally shines through, even though Church Fathers as far back as Jerome certainly knew this was happening and were able to reconcile it to their own faiths.

Quranic manuscript studies go just as deep. Despite what might be common knowledge about the Qur'an, there's actually multiple versions that have been historically accepted as authentic. This is primarily due to the fact that early Arabic script didn't include short vowel sounds and often lacked diacritics (dots) that clearly indicated differences between consonants. Early Muslims memorized the Qur'an and the text was only a memory aid, so this wasn't a problem at first. But eventually disputes arose, and so over the course of centuries, scholars compiled the different ways that diacritics and short vowels could be applied to the original script. This leaves some doubt as to which version of the Qur'an would have sounded familiar to Muhammad and his companions, although these versions aren't so radically different that they would challenge the integrity of the Muslim faith. However, when printed copies of the Qur'an began to circulate widely in the early 1900s, only one version was commonly printed. This remains the most common version and the basis for all English translations that I know of. So in this case, although Quranic studies have just as deep a tradition of philological analysis as biblical studies, it hasn't really been pursued among recent Western academics.

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A few things I'd recommend:

• Fred M. Donner, “From Believers to Muslims: Confessional Self-Identity in the Early Islamic Community,” Al-Abhath 50-1 (2003), 9-53. {This is a really important argument, but it should be read in the knowledge that not everyone agrees.}

• Hossein Modarressi, “Early Debates on the Integrity of the Qur’ān: A Brief Survey,”* Studia Islamica* 77 (1993), 5-39. {An interesting argument about how early Quranic studies helped lead to the Sunni/Shi'ite split}

• Gabriel Said Reynolds, ed., The Qur’ān in Its Historical Context, Routledge Studies in the Qur’ān (London: Routledge, 2008). {My comments mostly derive from the brilliant and concise introduction to this volume; most of the articles are similarly good, although a few chapters do seem to miss the mark.}

• Michael Sells, Approaching the Qur’an: The Early Revelations, 2d ed. (Ashland: White Cloud Press, 2007). {Read this before you read the Qur'an, or if you've read it and want to gain a better appreciation for its depth and beauty; one of the best books I've read.}