Lecture 2 - The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theorem of Algebra

Lecture 8 - Completion of the Proof of the Inverse Function Theorem: The Integral Inversion Formula for the Inverse Function

Lecture 12 - Proof of the Implicit Function Theorem: The Integral Formula for & Analyticity of the Explicit Function

Lecture 17 - The Riemann Surface for the functional inverse of an analytic mapping at a critical point

Lecture 18 - The Algebraic nature of the functional inverses of an analytic mapping at a critical point

Lecture 20 - General or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of Convergence

Lecture 23 - Continuity of Coefficients occurring in Families of Power Series defining Analytic Continuations along Paths

Lecture 24 - Analytic Continuability along Paths: Dependence on the Initial Function and on the Path - First Version of the Monodromy Theorem

Lecture 25 - Maximal Domains of Direct and Indirect Analytic Continuation: Second Version of the Monodromy Theorem

Lecture 26 - Deducing the Second (Simply Connected) Version of the Monodromy Theorem from the First (Homotopy) Version

Lecture 29 - Proof of the Algebraic Nature of Analytic Branches of the Functional Inverse of an Analytic Function at a Critical Point

Lecture 33 - Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-domains of the Unit Disc

Lecture 34 - Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc

Lecture 35 - Differential or Infinitesimal Schwarzs Lemma, Picks Lemma, Hyperbolic Arclengths, Metric and Geodesics on the Unit Disc

Lecture 38 - Arzela-Ascoli Theorem: Under Uniform Boundedness, Equicontinuity and Uniform Sequential Compactness are Equivalent