The Mind of God begins with physics, looking at different theories of the creation of the universe, the nature of physical laws and the possibility of a theory of everything. This leads on naturally to a discussion of mathematics and its philosophical foundations, and then on to computer science, and in particular the nature of computation and its relationship to physical processes. Then it's back to mathematics and its relationship with physics. After this things get more philosophical, with a look at various arguments for a "God" or at least something "outside" the universe. The final chapter is a look at mysticism and contains a suggestion that non-rational (religious and mystical) approaches to understanding may be able to go beyond the limits of physics.
The bulk of the material is expository, but Davies does come to two broad conclusions. The first is that there is something special about the universe, the second is that there is something special about us. "We are truly meant to be here." is the closing sentence of the book. I do not find the arguments for either of these at all convincing. I am tempted to play the positivist and argue that neither of his claims means anything (because I do not understand how anything can be "special" except to or for an observer, and hence cannot see how one can argue that the universe is special without first assuming the existence of a God), but there are other problems with these claims.
The argument that there is something mysterious about the universe is based on our ability to understand the universe at all and on its apparent operation according mathematical rules. The former is a natural consequence of our existence as intelligent animals, and the explanation of this is the task of evolutionary biology. (See below, and consult any work on the evolution of consciousness and cognition.) The latter is only significant if there is an alternative, and I would argue that anything with structure can have that structure represented mathematically, and anything that "exists" must connect to other things (perhaps there are invisible, intangible, non-interacting pink elephants out there, but they don't concern me) and hence must exhibit some kind of structure.
The laws of physics are indeed such as to allow life to exist, but it is not clear that we can deduce anything about our own significance from that. Even given the right laws of physics it seems that the existence of Homo sapiens (or indeed multicellular life) on this planet is a contingent fact of natural history and by no means inevitable. (See Stephen Jay Gould's Wonderful Life, for example.) Also, given that we do not even know what Omega (the average mass density of the universe) is to within an order of magnitude, it seems hard to argue for the sensitivity of the existence of life to the "initial conditions" of the universe!
The long progression through the arguments for the existence of God - the good old ontological argument, the cosmological argument and the argument from design all making their appearance - is a little odd. Davies provides more than adequate explanations for the failure of each of the different arguments as he proceeds, yet at the end has somehow given the impression that all the arguments put together, despite having been individually refuted, give some kind of support to there being a "God".
Davies' restriction of his view to the physical and mathematical sciences and his complete neglect of the historical sciences is also worrying. To me his ideas seem a strange mixture of Cartesian reductionism on the one hand and mystical idealism on the other. He attempts to reduce epistemology to physics, mathematics and computer science, and then, when these don't seem to be able to explain everything, resorts to appeals to mysticism and religion. There is more to the universe (and epistemology) than physics and mathematics deal with. Instead of looking to mysticism or religion for information about this or about our place in the universe, however, I would suggest trying anthropology and evolutionary biology.
These qualms about Davies' broader conclusions aside, The Mind of God is a brilliant exposition of foundational philosophical issues in mathematics, physics and computer science. It is recommended reading for anyone interested in the big philosophical questions.