Algebra of the Complex Plane, n-th root, definition of exponential functions and branches of logarithm. Topology of the complex plane (open, closed and connected sets, sequences, series and continuous functions). Holomorphic functions (Definition, Cauchy-Riemann Estimates, properties and examples). Complex Integration. Cauchy’s Theorem for triangles, Cauchy’s formula for simple contours and applications (Taylor expansion, calculating integrals, Liouville’s Theorem e.tc.), Cauchy’s formula for annulus and application (isolated singularities, Laurent expansion, calculation of real and complex integrals).