Power series: formal power series; convergent power series; analytic functions. Complex differentiation: holomorphic functions; Cauchy-Riemann equations; conformal transformations; elementary functions. Complex integration: integration along paths; primitives; Cauchy's theorem. Consequences of Cauchy's theorem: Cauchy's integral formula; holomorphic functions are analytic; further consequences (theorems by Morera and Liouville, mean value, maximum modulus, Weierstrass' convergence theorems). Singularities and residues: Laurent series; behavior near singularities; residue theorem and applications. Miscellanea: zeros and poles of meromorphic functions; Euler's Gamma function; analytic continuation.