Hermann Minkowski (1864-1909) was a prominent member of the famous golden epoch of mathematics at Gottingen University in Germany, which started with Karl Friedrich Gauss in 1807 and continued into the twentieth century (until the beginning of World War II). Minkowski is well known for his foundational work introducing the ""Minkowski spacetime"" in special relativity. He made significant contributions to number theory, especially in geometry of numbers and other topics. Minkowski was also known as an excellent teacher. The present book is an English translation of notes (never published) from the course on number theory taught by Minkowski in Winter 1907/08. The main topic of the course was the Fermat theorem and various methods used to prove it at that time. The translation is appended by the foreword written by John Little, who also edited the translation. The book can be helpful and interesting to students in number theory and to anyone interested in mathematics and its history.