This textbook provides an approach to differential and integral calculus that develops the associated theory based on content-related and intuitive considerations. The theory emerges as a refinement and as a means to overcome the limits of intuition. The book is aimed at students in teacher training for mathematics at the secondary level I, who require "Elementary Analysis" as a "higher perspective" for the study of functions, students in secondary school teacher training or in bachelor's programs seeking a meaningful approach to analysis, and mathematics teachers at the secondary level II who wish to design their analysis courses with a stronger focus on content rather than calculus. The development of the theory is complemented by fundamental considerations of functional relationships, mathematical foundations of analysis, as well as relevant applications in theory and practice.