Local theory Holomorphic function Cauchy-Riemann equations Conformal mapping Laurent series Meromorphic function Entire function Pole (complex analysis) Residue (complex analysis) Isolated singularity Removable singularity Essential singularity Weierstrass-Casorati theorem Contour integrals Path integral Cauchy integral theorem Cauchy's integral formula Residue theorem Liouville's theorem (complex analysis) Fundamental theorem of algebra Simply connected Winding number Bromwich integral Morera's theorem Special functions Exponential function Beta function Gamma function Riemann zeta function Riemann hypothesis Generalized Riemann hypothesis Elliptic function Growth Picard's theorem Value distribution theory of holomorphic functions Riemann surfaces Analytic continuation Riemann sphere Riemann surface Riemann mapping theorem Riemann-Roch theorem History (needs work) Bernhard Riemann Jacques Hadamard