The second volume of this textbook on analysis covers the material of the second semester of a mathematics foundational program for students of mathematics, physics, and computer science. The clear and structured layout takes into account that mathematical tools essential for understanding the fundamental physics lectures are discussed early on. Together with Volume 1, it serves as a guide for studying analysis, encompassing the mathematical foundational knowledge to be acquired in the first two semesters. Detailed proofs and explanations, along with numerous examples and interesting exercises, are well-suited for self-study. A clear and organized structure, along with a clever arrangement of the material, allows for a focus on core areas in the initial studies. Geometric intuition and historical motivation are interconnected.