John Freely has taught physics & history of science at Bosphorus University in Istanbul, so presumably he's in a good position to tackle the task indicated in the subtitle. Unfortunately, the book is only marginally successful. First, I expected the book to focus on the Islamic science that bridges the ancient world and modern science. Most histories of science don't spend much time on it, and it's easy to find yourself puzzeledly muttering, "What was the middle thing again?" Though Aladdin's Lamp certainly does better than that, Islamic science makes up less than half of the book, with the majority on ancient science and modern science (albeit with references to the trail through Arabic that connects one to the other).
Second, and worse, the book is not a very good history. Or rather, it's what we all thought history was when we were in third grade: a list of names and dates. There are some fairly long passages that are really no more than a paragraph or two about scientist A followed by two paragraphs about scientist B followed by... Rutherford once said that "All science is either physics or stamp collecting" -- in too many places, Aladdin's Lamp is the stamp collecting version of history of science. As just an example, we learn that "Hermannus is one of the earliest Latin authors to introduce to the Latin West three astronomical instruments that had been widely used in the Islamic world: the astrolabe, the chilinder, and the quadrant. ... All three instruments became widely used in the Latin West for astronomical observations as well as for calculations." One might (well I might) want to know what the hell a chilinder is. Or the astrolabe or quadrant, for that matter. Freely doesn't tell us. We might as well say that Hermannus "introduced the woozle, wozzle and wizzle to the West."
Nevertheless, the book does shed at least some light on that largely overlooked middle part, and a few interesting details about the two ends as well. Galileo is generally credited with the modern idea of inertia or momentum, but it was interesting to trace the history and development of essentially the right idea from the Greeks to Avicenna to Buridan to Galileo.
It's also fascinating how religiously diverse the scientific intelligentsia was during the height of Islamic science. Nestorian Christians fleeing persecution, Jews, Muslims, Zoroastrians, and a number of astronomers who were Sabians, a quasi-Islamic(?) religious sect that allegedly(?) worshipped the stars and planets.
Now if we can only convince Dar al-Islam to return to religious toleration, maybe the region can have another Golden Age. Unfortunately, it probably doesn't work that way, unless it comes with a side order of complete collapse of Western Society.