Philosophy begins in wonderment. Sometimes it ends there, too.
Good paradoxes aren't just for entertainment (although they _are_ vastly entertaining; check out any of Raymond Smullyan's books for proof of that assertion). Each of them opens a door to all sorts of fascinating issues of tremendous philosophical importance.
Mark Sainsbury's fine introduction, in its heavily revised second edition, is a set of keys to those doors. For example, his discussion of Zeno's famous paradoxes doesn't just inform the lay reader what they are; it explains why they're important even today: because they call into question whether the now-standard mathematical analyses of the paradoxes adequately capture our ordinary understanding of space. That is, the paradoxes can be resolved in the ideal space of mathematicians, but that doesn't _necessarily_ mean they can be resolved in the space in which we really live.
In difficulty, the exposition is about one notch higher than in William Poundstone's _Labyrinths of Reason_, so you may want to read Poundstone first if you're new to this subject altogether. But do get around to this one. It's a solid account, from a more or less "analytic" outlook (though that term probably suffers from all the "vagueness" problems discussed in Sainsbury's second chapter).
Sainsbury will also introduce some topics Poundstone doesn't cover -- notably, and perhaps most interestingly, Graham Priest's "dialethism" -- a logic in which, Priest claims, it's possible for some contradictions to be true[!]. Sainsbury doesn't agree but nevertheless concludes that he doesn't have a knockdown argument against it. (Be aware that Sainsbury's account has been criticized by other philosophers, including Priest. Follow up with Priest's own books if you get interested in this subject.)
Sainsbury also doesn't hesitate to offer his own resolutions of the paradoxes, but he warns the reader not to accept his resolutions blindly. In fact there are several about which I continue to disagree with him (not an unusual phenomenon when the subject is paradoxes), but he's changed my mind on a couple.
Overall, then, this is a well-written and cogently argued presentation, highly recommended to anyone interested in paradoxes and their relevance to philosophy.