I support very much the idea to recommend the Fuks and Tabachnikov book as in the answer above, and in addition to this two book by Vladimir Arnold:
Arnold's problems book for school students, which is freely available via http://imaginary.org/sites/default/files/taskbook_arnold_en_0.pdf . Note that it is also available in many languages on the same web site.
Arnold's Catastrophy Theory, which gives a great introduction to dynamical systems and related topics.