Supremum, infimum, limsup, liminf. Cauchy completeness of the real numbers, order completeness, Archimedean property. Series of numbers, ratio and root tests in terms of limsup, liminf. Condensation and Raabe tests. Alternating series, rearrangements, products of series. Topology of R² and R³. Convergences and continuity of functions of several real variables. The concept of metric space. Metrics on Rⁿ, Holder – Minkowski inequalities. Open and closed sets, interior and closure. Continuous functions. Complete metric spaces, sequences of nested closed sets, Cantor’s theorem. Banach’s fixed-point theorem. Applications: Picard’s theorem, implicit function’s theorem.