[jonp]

"1089 and all that" by David Acheson is charming and very readable. It covers a variety of different types of maths but more importantly get across what maths is really about. I've bought it for friends and family with a wide range of maths backgrounds (graduate mathematicians to not-since-school-forty-years-ago).

Also "Alice and Numberland", Baylis and Haggarty; and "The Foundations of Mathematics", Stewart and Tall. These are both pitched somewhere between high school and university level and bridge the gap well.