For a list of recommended books for young people interested in Mathematics, try this list from Nrich which is grouped into three different categories: History of Mathematics, Recreational and Thinking Mathematically.

From Cambridge University this list of interesting mathematics books and internet sites is mainly intended for sixth-formers planning to take a degree in mathematics. The list includes some items which are suitable for less experienced readers so may well appeal to a wider audience. The list was last updated in September 2020. I see it includes Kevin Houston’s “How to Think Like a Mathematician, see also from Kevin Houston his page on the book which includes some solutions to problems in the book, also available are sample chapters on writing mathematics.

See the Reference page also which includes a useful list of reference materials.