There are now almost exactly 20 years since I wrote the lecture notes that eventually became this book. In the meantime, great progress has been made in virtually all branches of mathematics and number theory is no exception. In the elementary part (covered, essentially, in the first seven chapters)» definitive theorems had been known since the time of Euler or even Fermat, and there the new results are of rather minor importance (new Mersenne primes, more stringent conditions for the highly unlikely existence of odd perfect numbers, better terms in "elementary" proofs of the Prime