I rate this along with Penrose's The Emperor's New Mind: Concerning Computers, Minds and the Laws of Physics (Popular Science)
as being on the exact borderline between popular science and the domain of the serious practitioner. If you've got a bit of rusty old undergraduate maths, and you want to engage with some fascinating science that they didn't teach you in school/college, then you should just about be able to hang on for this exhilarating ride.
It's a tour of physics, all of science in fact, but arranged sort of transversely to the usual treatments, in such a way as to illustrate the numerous ways in which anthropic thinking impacts on modern science. So it's as much a philosophy of Physics as a straight physics text.
So starting from the very beginning, we look at all the infinitude of ways the big bang might have worked out: from universes so brief or tiny as to be 'pointless', to those that don't have a sufficient preponderance of matter or anti-matter, and so end up too empty to be interesting. However, we thinking beings find ourselves in a Goldilock's universe that's 'just right', and we examine the exquisitely tuned parameters required for this to be so.
Next we look at how gravity is arranged 'just right' so as to make galaxies, stars and planets, rather than an endlessly dissipating cloud of fog, or at the other extreme, a universe of nothing but black holes.
We then move on to the nuclear forces and find all the ways it might have been whereby there was nothing more interesting than hydrogen, or helium, or nitrogen, or carbon, or where all there is iron, and so on. But again we find ourselves in the Goldilock's universe, where the exquisitely tuned parameters of the nuclear forces allow the stars to ignite and turn simple nuclei into a rich variety of other nuclei, which in turn provide the basis of a chemistry interesting enough for life to develop.
And so on up the chain of being we go. Quantum parameters that allow chemistry interesting enough to make molecules, that are in turn interesting enough to make biological processess possible. The ludicrous unlikelihod of a molecule that can self-replicate (DNA), and not just that, but that can interact with other ludicrously unlikely molecules to reliably build intricately structured proteins, and so on.
We study planets and the rather narrow range of size/masses they must have in order to retain atmospheres and liquid oceans, and allow complex organisms to stand up and move around without falling apart or drifting off into space. We consider why carbon based life forms are the most likely sort, because no other atom has chemistry interesting enough to generate the huge range of macromolecules upon which biology depends.
We look at all the alleys that evolution explored before it got around to trying the big brain strategy, and speculate a bit on how big a brain has to be before it can start reflecting on the structure of the universe it finds itself in, thus finally coming round to framing the anthropic question: how we thinking beings come to find ourselves living at a place and time capable of supporting thinking beings? Along the way we have watched the probabilities against such a universe stack up in a geometric series of infinitesimals.
We then explore the ramifications of the anthropic principle and its various weak to strong flavours. From the position whereby this one and only exquisitely tuned universe implies a Designer God, but also observing that the Designer God is as ludicrously improbable as the Universe its supposed to explain. At the other extreme we have the position that all Universes that can be, are, and its simple logical necessity that we thinking beings find ourselves in one of the tiny subset that can support thinking beings. There is in fact a beautiful little book by the philosopher John Leslie Universes
which I found an excellent follow up to this aspect of anthropic thinking. Leslie is a theist, but presents the ramifications of the anthropic principle systematically, and makes clear that there is no final clincher in cosmology to determine the correct position.
The last couple of chapters are more speculative, and include the speculations of Brandon Carter, arguably the father of modern anthropic thinking and Tipler's more infamous conjectures about omega points, immortality, total universal intelligence and so on. The author's make clear that these are speculations, and that they are above all good fun to think about. Unfortunately, more credulous theorisers have latched on to some of these notions in such a way as to give anthropic thinking a bad reputation amongst the more sober science community. A shame, because there are some serious questions to be answered there.