This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivatingdefinitions, results and proofs. Simple examplesare provided toillustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Walliss formula and Stirlings formula, proofs of the irrationality of and e and a treatment of Newtons method as a special instance of finding fixed points of iterated functions.