Richard Swinburne doesn't need to be introduced to those interested in contemporary philosophy of religion. He is - together with Alvin Plantinga - the finest living analytic christian philosopher. He opens this book with a statement that "the book aims to discuss the topic [i.e. whether or not there is a God] in depth and with rigour" and this is just what he does.
Swinburne builds a probabilistic case for theism while rejecting deductive arguments. He treats theism as a quasi-scientific hypotheses. His method is quite simple. After a few introductory chapters, he tries to make some a priori considerations about what is to be expected if there is a God. He then examines various features of the universe (as well as its existance) and shows that these are more to be expected if there is a God than if there is no God. To use the standard symbols, he argues that P(e/h&k)>P(e/~h&k), where P(e/h&k) means probability of e given h and k (e is the evidence that Swinburne considers, h is theism, ~h is "theism is false" and k is previously considered evidence). From this it follows that P(h/e&k)>P(h/k), so each piece of evidence increases the probability of theism. Probability here is to be understood as the degree of confidence to which we can suppose that something is true (so called epistemic probability).
Swinburne also adresses the objection that his arguments could be as well used to show that there are a few minor deities or one deity with great but limited power and wisdom. His refutation of these charges is brilliant (but also controversial).
Swinburne also raises the problem of evil, but his discussion of this issue is - I think - the weakest part of the book. He concludes that evil decreases the probability of theism, but only slightly. His refutation of the argument from hideness against the existance of God is compelling.
In the last chapter of the book, trying to reach some more definite conclusions, Swinburne faces a huge problem - so far he showed that various pieces of evidence he considered are such that each (apart from evil) increases the probability of theism, some moderately and some considerably. But to reach some value, we have to start with something. And what value should we start with? Any value of P(h/k) (intrinsic probability of theism or - as the author says - probability on tautological evidence) seems completely arbitrary and unjustified. Here once again Swinburne comes up with an excellent solution.
It's worth noting that Swinburne's concept of God is not identical with the traditional views on God - He is not a logically necessary being, He exists eternally in time and He doesn't know what a free creature will do (since - according to Swinburne - this is logically impossible; so of course God is nevertheless omniscient). Neither is He the source of moral truths. Readers interested in philosophy of religion will by acquainted with authors positions on these matters. Anyway, it doesn't make much difference to the argument (apart from necessity - if you think God is logically necessary, then a supposition that there is no God is incoherent, so it's obvious that P(e/h&k)>P(e/~h&k) since the latter is zero,if any at all)
So there are some controversial points. Nonetheless, this is probably the strongest argumentation for theism ever written. It is precise and rigurous. And I think the conclusion ("theism is more probable than not") is sound, as long as you accept what the author calls the "principle of simplicity", which seems right (but is far from uncontroversial- Platinga for example doesn't accept it, as fas as I know). But I suppose I would give 5 stars even if I didn't agree with the conclusion - that's because this is one of the most important books in contemporary philosophy of religion, an enormous contribution to natural theology. And its general approach is (or was when published) a novelty in this field. It is a must for anyone seriously pondering the question of the justification of belief in God.
The argument is continued in "Revelation" and in "The Ressurection of God Incarnate".