This book is the companion volume of "The Elements of Mathematics from a Modern Viewpoint I", which contains about 1000 problems on the various subjects. Volume II recalls these problems and provides detailed solutions of most of them. As in Volume I, the problems are presented here in yellow frames. The most difficult problems, intended for the "very curious students" are given in green frames surrounded by a wiggly border. The wiggly border is intended for the color blind students. This volume also recalls some of the definitions which are critical to the solutions of the problems. There is an appendix, which reviews the units of length, mass, capacity, and time because those concepts are used in the statement of the problems.