We present here the English version of the Romanian first edition (V. Berinde: Ex plorare, investigare si descoperire in matematica, Editura Efemeride, Baia Mare, 2001). There are no major changes. Only a few printing errors were corrected. When transcribing Romanian names or denominations we did not use the diacrit ical marks. Our purpose is to provide an introduction to creative problem solving tech niques with particular emphasis on how to develop inventive skills in students. We present an array of 24 carefully selected themes that range over all the main chapters in elementary...