Rebuilding the calculus building -- The real number system revisited -- Sequences and series of real numbers -- Limit and continuity of real functions -- Derivative and differentiation -- The Riemann integral -- Abstraction and generalization -- Basic theory of metric spaces -- Sequences in general metric spaces -- Limit and continuity of functions in metric spaces -- Sequences and series of functions -- Appendix -- Real sequences and series -- Limit and continuity of functions -- The concepts of derivative and differentiability -- The Riemann integral