Convergence of sequences and series of complex numbers, notion of Cauchy sequence and of complete metric space, uniform convergence, power series, the Abel limit theorem, analytic functions and Taylor series, zeros of analytic functions, analytic functions uniqueness theorem, Parseval formula for power series, Cauchy estimates, Liouville theorem, maximum modulus principle. Exercises, including on Bernoulli numbers and with applications to hydrodynamics, electrostatics, and heat propagation in equilibrium.