Anticlaudianus is about the nature of reason, so the work is technically a treatise on epistemology, or the study of knowledge and belief. Some of the basic fundamental assumptions we hold about the universe today was not obvious almost a thousand years ago (Alan of Lille lived in the mid 1100's). Consider also that the institution of the university was recent during his time, and his studies in Paris were absolutely formative in his approach to philosophy. Essentially, Alan believed that every belief necessitated an explanation, and since some concepts are not communicable, they must fall outside the bounds of reason.
Here is the central axiom of Anticlaudianus, paraphrased: Ethical, honest reasoning can discover most of the knowable aspects of the universe. This commitment to logic and observation are the fundamental aspects of the scientists from a few hundred years in Alan's future. For instance, Bacon would likely believe the same way that Alan believed about epistemology. They both believed that we could trust our senses and our instincts, and that the primary way we should focus our reasoning is the realm of concrete fact.
This work is the beginning of a long, tedious discussion, and there have been many, many thinkers who have debated the nature of reason and faith, back through Plato and up to the present day. Needless to say, these ideas may seem obvious to a modern person, but philosophically, the ideas are hard to sort out, and actually, the longer we study, the more complex it gets, so there is still much work to be done answering Alan's arguments.