After completing his famous Foundations of Analysis (See AMS Chelsea Publishing, Volume 79.H for the English Edition and AMS Chelsea Publishing, Volume 141 for the German Edition, Grundlagen der Analysis), Landau turned his attention to this book on calculus. The approach is analytical, with an emphasis on functions rather than on geometric or physical applications. Providing an example of Landau's formidable skill as an expositor, this text is a masterpiece of rigor andclarity.