A brilliantly refreshing, readable and clear run-through of the history of religion and mysticism, mostly Christianity, and looking more at the writings of scholars rather than the experience of the laity. Armstrong doesn't really make a case for God (as in the existence of God) but rather a case for the argument that we cannot know anything about God. She clearly explains why any attempt to understand God intellectually, or to define "him", is pointless and tends to lead to idolatry. Her argument is that seeking to define the nature of God is largely a product of the scientific age, but her evidence for a more uncertain approach to God being typical previously comes from the writings of certain Greek and early Christian mystics, which she paints as typical of their times, rather than unusual - something I'm not in a position to verify.
Importantly, she argues that religion is a matter of practice not "belief" (a word that now means an acceptance of something as fact, but which in the past had the connotation more of commitment, like love), and that where it is entered into, it is best done with the understanding that it is not based on any knowledge of God's nature.
This book could be seen as an argument for mysticism, but there is no attempt at conversion here. The book doesn't itself suggest why someone not already on a religious path should follow one. Religious practice might be rewarding, but no one could be expected to know that until they were well on it, after much hard work they could otherwise have avoided. My reading of the book is that those disposed to religious practice (by circumstances, upbringing or genetics) should follow the one that best suits them, but on the understanding that the choice of practice itself is of little consequence, as long as it is entered into without any belief in its factual superiority. Meanwhile, those not so disposed to do so, should not be expected to. In the end, it is an erudite plea for a greater acceptance of the state of Unknowing. Whether such a plea will find many listeners in an age where factual knowledge and certainty are held in such high regard remains to be seen.