This is a course on the theory of differential and integral calculus of one or several real variables. It is based on rigorous theory and state-of-the-art methodology. Topics include: differentiability in one or higher dimensions, mean-value theorem, Taylor theorem, convexity; integrability in one or higher dimensions, fundamental theorem of calculus, improper integrals, Fubini’s theorem for double series and continuous functions; power series, radius of convergence, series for elementary functions, real analyticity; sequence and series of functions, uniform convergence.