Hume begins by outlining that while most religions today are monotheistic, this was not was religion was in its earliest stages of development. Rather, the first religions that mankind had were polytheistic religions, and rather than being all powerful, they were capricious and not very caring about people. Hume also notes, and here he disagrees with Irish philosopher Edmund Burke, that some cultures have shown no belief in religion or God at all, showing that perhaps man is not always a religious animal as Burke believed.
One of the questions that Hume addresses throughout the book is that mankind seems to show a belief in invisible power or agency, and from this comes mans belief in fairies, goblins, demi-gods, and then the traditional monotheistic God. Hume is unknowingly laying in some degree the foundation for modern evolutionary theory, showing that man goes from brute, unintelligent beginnings until he reaches the station where he is now.
While Hume does criticize religion in the book for the harm it has done in the past and present, do not come away with the idea that Hume is an atheist, because he simply isn't. In the book he states that Christianity is the only religion that is free of contradiction, and that the design in the cosmos show the handiwork of an intelligent creator and author. However, Hume does state that in large part most religious belief comes from a dread of the unknown. For instance:
"It must necessarily, indeed, be allowed, that in order to carry men’s attention beyond the present course of things, or lead them into any inference concerning invisible intelligent power, they must be actuated by some passion which prompts their thought and reflection; some motive which urges their first inquiry. But what passion shall we here have recourse to, for explaining an effect of such mighty consequence? Not speculative curiosity surely, or the pure love of truth. That motive is too  refined for such gross apprehensions, and would lead men into inquiries concerning the frame of nature; a subject too large and comprehensive for their narrow capacities. No passions, therefore, can be supposed to work upon such barbarians, but the ordinary affections of human life; the anxious concern for happiness, the dread of future misery, the terror of death, the thirst of revenge, the appetite for food and other necessaries. Agitated by hopes and fears of this nature, especially the latter, men scrutinise, with a trembling curiosity, the course of future causes, and examine the various and contrary events of human life. And in this disordered scene, with eyes still more disordered and astonished, they see the first obscure traces of divinity."The book concludes that while religion is based on fear and a dread of the unknown, that is not the same as belief in God. To quote Hume again:
"The universal propensity to believe in invisible, intelligent power, if not an original instinct, being at least a general attendant of human nature, may be considered as a kind of mark or stamp, which the divine workman has set upon his work; and nothing surely can more dignify mankind than to be thus selected from all the other parts of the creation, and to bear the image or impression of the universal Creator. "While Hume is happy to admit that God exists, he does not believe humans can understand his nature or attributes, and calls the caricatures that men have mad of God "sick men's dreams"
Anyone interested in the study of religion should definitely have a copy of The Natural History of Religion in there collection. However, one caution I would make is that while Hume was a man of the enlightenment, his racism and prejudices are sometimes painfully obvious in the text. However, it is overall a very good introduction to religious anthropology. 4 out of 5 stars.