Very well-written, and it flows past as you read it very nicely. The four stars come mainly from that, and from the courage even to tackle so vast a subject. However its interest comes more from seeing what Karen Armstrong's view is, rather than on the content of what she says as such. She covers a vast range of material and history, but regarding the areas about which I know a little, her views are often highly idiosyncratic.
For example, she spends a long time discussing Sparta as a model of Greek cities, whereas Sparta was almost as exceptional in Greece as it was of any other society past or present. Her idea that justice became completely arbitrary under Athenian democracy is also an extremely exceptional view. She emphasises the role of slavery in Greece, without mentioning that Persia, India and China, with which she is making a comparison, had much greater slavery and less freedom.
Similarly, stating as a fact that Laozi wanted to use contradictions as a way of inducing people use mystical insight rather than rational logic, is also another oddity. There are many more conventional ways of taking Laozi and it would have been better if she at least mentioned other approaches.
Most illuminating of all is her view that Mohammad was the "last flowering of the Axial age". It is hard to say, given that she has already extended the era 800 years, why she doesn't continue with subsequent thinkers in the tradition, such as al-Hakim or the Sikh gurus or even Bahaiullah or Hazrat Inayat Khan. What is interesting here is the limit she puts on her ecumenicalism. The Axial age sages are recognised by most Muslims as earlier prophets. However, normally, only an orthodox Muslim would consider Mohammad to be the "last".