This book is intended as a teacher's manual of Number Theory and a self-study handbook for high-school or college students, and mathematical competitors. The book teaches new and classical proof techniques of Number Theory through practical and challenging problems. It is arranged by topics and difficulty level.It mainly consists of new problems created by authors with author-prepared-solutions, some of these problems were proposed in different national and international Mathematical Olympiads from 1984 to 2018.The book gives a broad view of Number Theory and goes beyond the typical elementary mathematics by providing deeper treatment of the topics.About the authors.Hayk Sedrakyan is an IMO medal winner, Professor of mathematics in Paris, France and a professional Math Olympiad Coach in Greater Boston area, Massachusetts, USA. Having served as a Team Leader at Harvard-MIT Mathematics Tournament (HMMT) and as a scientific researcher at the European Commission. He has defended his PhD thesis in mathematics in UPMC-Sorbonne University, Paris, France.Nairi Sedrakyan is involved in national and international Olympiads of mathematics, having been the President of Armenian Mathematics Olympiads and IMO jury member. He is the author of one of the hardest problems ever proposed in the history of IMO (5th problem of 37th IMO). Students of Nairi Sedrakyan have obtained 20 Gold, Silver and Bronze medals in IMO, providing more than half of the medals that Armenia received in the history of its participation in IMO (till that year). For his outstanding teaching Nairi Sedrakyan received the title of the best teacher of the Republic of Armenia and has been awarded with a special gift from the Prime Minister.