Ibn Khaldun, The Muqaddimah — The greatest work of medieval Islamic historiography was written by Ibn Khaldun, who was born in Tunis and spent time in Kairouan's intellectual orbit. His introduction to his world history covers the rise and fall of dynasties, the nature of urban civilization, and the recurring cycle of nomadic conquest — themes that run through the history of Kairouan itself. Not light reading, but genuinely illuminating.
Paul Sebag, Tunis: History of a City — A thorough account of Islamic North Africa centred on Tunis, but with much material on Kairouan's role as the founding capital of Arab North Africa. Sebag writes clearly about the Aghlabid and Fatimid periods, which are the critical chapters in Kairouan's story.
Robert Irwin, Islamic Art in Context — A scholarly but accessible introduction to Islamic decorative arts that will sharpen your appreciation of the Mosque of the Three Doors facade and the Zaouia of Sidi Sahab tilework considerably. Irwin explains the logic of Islamic ornament — why it takes the forms it does, what it is doing — in a way that transforms looking at these buildings from passive tourism into active understanding.