Charles-Andre Julien's History of North Africa: From the Arab Conquest to 1830 is one of those good introductory overviews for the history of the Maghrib. Unfortunately leaving out Libya, which is our primary area of interest for North Africa, Julien covers the rest of the region from the Arab conquests to the 19th century. Beginning with the Byzantine period and the lengthy Arab conquests and spread of Islam, the book then shifts to the major Islamic dynasties and states which dominated parts of North Africa, like the Aghlabids, Imams of Tahert, Fatimids, Hafsids, Alawi dynasty, Almohads, Almoravids, and Regencies of Algiers and Tunis.
We can't lie, sometimes one gets lost in the various names and dynasties over 1000 years. But Julien mostly retains the reader's interest and occasionally delves into other topics, like the spread of Islam, Sufism, the Barbary corsairs, the political economy of Tunis and Algiers, and how the Sharifian dynasties held Morocco together. Since the text was originally published several decades ago, we're sure that archaeologists and historians have shed more light on the Arab conquest and perhaps today's scholars would avoid phrases like "Berber inertia" to characterize what Julien describes as societies trapped in a civilization that hadn't changed much since the 7th or 8th centuries.
Moreover, it would be interesting to read a history of North Africa that attempts to integrate a Saharan and Mediterranean perspective on the region. Julien, of course, mentioned the Moroccan invasion of Songhay and Hafsid relations with Kanem, but he seems to have bought into the idea that the Islamic civilization of the Sahel was an implanted Maghribi one while also minimizing the importance of the trans-Saharan trade. We have a lot more books to complete on North Africa before we can explore this, but we know Braudel will be on our reading list to help us understand the Mediterranean and, perhaps, how the Saharan "sea" was connected to it.