It was written by Lasse Rempe-Gillen and Rebecca Waldecker, and originally published in German as Primzahltests für Einsteiger: Zahlentheorie, Algorithmik, Kryptographie (Vieweg+Teubner, 2009).
Primality Testing for Beginners has seven chapters, divided into two parts: four chapters on background material in number theory and computational complexity theory, and three on the AKS primality test.
[1][5] Chapter 1 includes basic material on number theory, including the fundamental theorem of arithmetic on unique factorization into primes, the binomial theorem, the Euclidean algorithm for greatest common divisors, and the sieve of Eratosthenes for generating the sequence of prime numbers.
[5] Both the correctness and the polynomial running time of the algorithm are proven rigorously.
[4] Reviewers Robin Chapman and Jeffrey Ehme agree that the overall content of the book is probably too slight to use it as the main textbook for an undergraduate number theory course, but that it could be a good supplement for such a course, or for a course in cryptography.