The following is a list of fundamental theorems in the subject of complex analysis (single complex variable). If a theorem does not yet appear in the encyclopedia, please consider adding it -- Planet Math is a work in progress and even some basic results have not yet been entered. Likewise, if some basic theorem has been overlooked in this list, please add it.

• Cauchy-Riemann equations
• Cauchy's integral theorem
• second form of Cauchy integral theorem
• Morera's theorem
• Cauchy's integral formula
• Cauchy's residue theorem
• Cauchy's argument principle
• Rouché's theorem
• identity theorem of power series
• rigidity theorem for analytic functions
• Riemann's removable singularity theorem
• Casorati-Weierstrass theorem
• implicit function theorem for complex analytic functions (I gave proofs of this and the next theorem in a posting to a forum and must convert them to an encyclopaedia entry.)
• inverse function theorem for complex analytic functions
• maximal modulus principle
• Schwarz lemma
• Liouville's theorem
• characterization of rational functions
• Weierstrass' factorization theorem
• Weierstrass' criterion of uniform convergence
• Mittag-Leffler's theorem
• Möbius circle transformation theorem
• Riemann mapping theorem
• Gauss' mean value theorem
• Schwarz' reflection principle
• Harnack's principle
• Bloch theorem
• Picard's theorem
• Little Picard theorem
• Monodromy theorem
• Runge's theorem
• Mergelyan's theorem
• Montel's theorem
• Marty's theorem
• Hurwitz's theorem
• Bieberbach's conjecture
• Koebe one-fourth theorem
• Factorization theorem for $H^\infty$ functions
• Plemelj formulas
• Harnack theorem
• Schwarz and Poisson formulas