The paradox arises in a game show in which the prize is hidden behind one of three doors. You pick one, and then Monty, the game show host, opens one of the other doors and shows you that the prize is not behind it. He then asks if you want to change your mind and pick a different door or stick with your original choice. Most people elect to stick, but in fact their chance of winning is greater if they switch.
Al-Khalili gives the clearest explanation of this that I have seen. He shows that the critical element in the puzzle is that Monty knows which door conceals the prize. This fact is what weights the probability in favour of switching. He illustrates this by considering what would happen if you played the game 150 times; your chance of winning changes according to whether Monty knows or doesn't know where the prize is located. (In the real game, of course he does know, and this is what makes the difference.)
Subsequent chapters deal with Achilles and the tortoise (again a mathematical or logical puzzle rather than a physics one). Olber's paradox, Maxwell's demon, the pole in the barn (a puzzle depending on Einstein's Special Relativity), the twins' paradox (Einstein again), the grandfather paradox (what would happend if you went back in time and killed your grandfather?), Laplace's demon (is the future totally predictable in principle?), Schrödinger's cat, and Fermi's paradox (if there are aliens why haven't they visited us?).
In his concluding chapter Al-Khalili looks at some questions that don't (yet) have a solution. He places these in three categories: ten that he thinks will be solved in his lifetime, ten that he is confident science will answer although probably not in his lifetime, and four that are probably within the scope of science but may never be answered. This last group includes: Do we have free will? Are there parallel universes? What caused the Universe to come into existence? Did we invent mathematics to describe the Universe or were the equations out there just waiting to be discovered?
The free will question is discussed in the chapter on Laplace's demon. Al-Khalili favours the view that determinism is true but that free will is rescued by chaos theory (not by quantum mechanics, as some believe). Chaos theory implies that the future is never totally predictable. This is at best a qualified sort of freedom, as Al-Khalili admits. "Whether we call it true freedom or just an illusion in a way does not matter." (For more on this question, see Galen Strawson, Freedom and Belief, Robert Kane (ed.), The Oxford Handbook of Free Will), and Daniel M. Wegner, The Illusion of Conscious Will.)
25 May 2014