This book sets itself apart from most, if not all, the other books because it offers narrative analysis and solutions to many of the world's toughest mathematical problems used in the international and national competitions around the globe. At the time of this book's publication, solutions to many of these problems had not been found anywhere. Moreover, this book translates these seemingly the most prestigious and difficult problems into understandable terms, and thus making itself a highly valuable reference material for educational use. This book is written in a way that it would actively help a general audience learn the concepts and foundations of higher mathematics. It is a must read for many students and a useful tool for teachers around the world. It is not easy to write a mathematical book with solutions to many difficult problems, especially the ones that had not been solved for so long, because problem solving requires reasoning, the ability to formulate, represent and connect the existing mathematical theorems, lemmas, corollaries and laws to succeed, and that is why there is this book.