Book recommender systems provide personalized recommendations of books to users based on their previous searches or purchases. As online trading of books has become increasingly important in recent years, artificial intelligence (AI) algorithms are needed to recommend suitable books to users and encourage them to make purchasing decisions in the short and the long run. In this paper, we consider AI algorithms for so called collaborative book recommender systems, especially the matrix factorization algorithm using the stochastic gradient descent method and the book-based k-nearest-neighbor algorithm. We perform a comprehensive case study based on the Book-Crossing benchmark data set, and implement various variants of both AI algorithms to predict unknown book ratings and to recommend books to individual users based on the highest predicted ratings. This study aims to evaluate the quality of the implemented methods in recommending books by using selected evaluation metrics for AI algorithms.