Completed in A.D. 972 (at the same time as the then-new city of Cairo), this mosque has since undergone many renovations, restorations, and additions. And though it may not be the most architecturally interesting mosque in the city, it's certainly the most politically significant. Since A.D. 988, it has also been the center of the most prestigious university in the Islamic world. The mosque itself is at the center of a sprawling and diverse campus more or less invisible to the casual observer because of the way it's woven into the fabric of the neighborhood. There are nine other campuses around Egypt, and the total student body, which includes many international students, is more than 100,000. Moving with the times, at least in form, it now teaches a fairly full curriculum of modern courses (including medicine), as well as the more traditional theological studies. It also has a women's annex.
Visitors should be particularly aware of religious sensitivities here. Women should wear clothing that covers the arms, legs, and shoulders, and should cover their heads with a veil. Scarves and burqas are available at the entrance for those who aren't carrying something with them, and both men and women need to remove their shoes at the entrance. The mosque has been the focal point of periodic anti-government demonstrations in the past, and visitors should particularly avoid Friday prayers here.
Inside is a mix of the original architecture and subsequent additions. For example, the central courtyard that you see as you enter is to the original dimensions, but the roundels and arches were added as part of a 12th-century renovation. Inside, the Kufic lettering around the mihrab is original, but much of the decorative stucco work was added in the early 14th century.
There are usually a number of fairly well-mannered students relaxing in the mosque reading or chatting with friends, and you may find yourself being offered guiding service. As with almost everywhere in Egypt, expect to be hit up for a tip at the end of the tour. I would give LE5 (90¢/45p) if the tour has been interesting and worthwhile; LE2 (36¢/19p) would be quite sufficient if you just want to get rid of them.