Introduction -- Familiarization with semi-normed spaces -- Notations -- Prerequisites -- Semi-normed spaces ; Semi-normed spaces -- Comparison of semi-normed spaces -- Banach, Fréchet and Neumann spaces -- Hilbert spaces -- Product, intersection, sum and quotient of spaces -- Continuous mappings ; Continuous mappings -- Images of sets under continuous mappings -- Properties of mappings in metrizable spaces -- Extension of mappings, equicontinuity -- Compactness in mapping spaces -- Spaces of linear or multilinear mappings -- Weak topologies ; Duality -- Dual of a subspace -- Weak topology -- Properties of sets for the weak topology -- Reflexivity -- Extractable spaces -- Differential calculus ; Differentiable mappings -- Differentiation of multivariable mappings -- Successive differentiations -- Derivation of functions of one real variable.