Lecture 1 Play Video 
Properties of the Image of an Analytic Function: Introduction to the Picard Theorems

Lecture 2 Play Video 
Recalling Singularities of Analytic Functions: Nonisolated and Isolated Removable

Lecture 3 Play Video 
Recalling Riemann's Theorem on Removable Singularities

Lecture 4 Play Video 
CasoratiWeierstrass Theorem; Dealing with the Point at Infinity

Lecture 5 Play Video 
Neighborhood of Infinity, Limit at Infinity and Infinity as an Isolated Singularity

Lecture 6 Play Video 
Studying Infinity: Formulating EpsilonDelta Definitions for Infinite Limits

Lecture 7 Play Video 
When is a function analytic at infinity?

Lecture 8 Play Video 
Laurent Expansion at Infinity and Riemann's Removable Singularities Theorem

Lecture 9 Play Video 
The Generalized Liouville Theorem: Little Brother of Little Picard

Lecture 10 Play Video 
Morera's Theorem at Infinity, Infinity as a Pole and Behaviour at Infinity

Lecture 11 Play Video 
Residue at Infinity and Introduction to the Residue Theorem for the Extended

Lecture 12 Play Video 
Proofs of Two Avatars of the Residue Theorem for the Extended Complex Plane

Lecture 13 Play Video 
Infinity as an Essential Singularity and Transcendental Entire Functions

Lecture 14 Play Video 
Meromorphic Functions on the Extended Complex Plane

Lecture 15 Play Video 
The Ubiquity of Meromorphic Functions

Lecture 16 Play Video 
Continuity of Meromorphic Functions at Poles and Topologies

Lecture 17 Play Video 
Why Normal Convergence, but Not Globally Uniform Convergence,

Lecture 18 Play Video 
Measuring Distances to Infinity, the Function Infinity and Normal Convergence

Lecture 19 Play Video 
The Invariance Under Inversion of the Spherical Metric on the Extended Complex Plane

Lecture 20 Play Video 
Introduction to Hurwitz's Theorem for Normal Convergence of Holomorphic Functions

Lecture 21 Play Video 
Completion of Proof of Hurwitz\'s Theorem for Normal Limits of Analytic Functions

Lecture 22 Play Video 
Hurwitz's Theorem for Normal Limits of Meromorphic Functions in the Spherical Metric

Lecture 23 Play Video 
What could the Derivative of a Meromorphic Function

Lecture 24 Play Video 
Defining the Spherical Derivative of a Meromorphic Function

Lecture 25 Play Video 
Welldefinedness of the Spherical Derivative of a Meromorphic Function

Lecture 26 Play Video 
Topological Preliminaries: Translating Compactness into Boundedness

Lecture 27 Play Video 
Introduction to the ArzelaAscoli Theorem

Lecture 28 Play Video 
Proof of the ArzelaAscoli Theorem for Functions

Lecture 29 Play Video 
Proof of the ArzelaAscoli Theorem for Functions

Lecture 30 Play Video 
Introduction to the Montel Theorem

Lecture 31 Play Video 
Completion of Proof of the Montel Theorem

Lecture 32 Play Video 
Introduction to Marty's Theorem

Lecture 33 Play Video 
Proof of one direction of Marty's Theorem

Lecture 34 Play Video 
Proof of the other direction of Marty's Theorem

Lecture 35 Play Video 
Normal Convergence at Infinity and Hurwitz's Theorems

Lecture 36 Play Video 
Normal Sequential Compactness, Normal Uniform Boundedness

Lecture 37 Play Video 
Local Analysis of Normality and the Zooming Process  Motivation for Zalcman's Lemma

Lecture 38 Play Video 
Characterizing Normality at a Point by the Zooming Process

Lecture 39 Play Video 
Local Analysis of Normality and the Zooming Process  Motivation for Zalcman\'s Lemma

Lecture 40 Play Video 
Montel's Deep Theorem: The Fundamental Criterion for Normality

Lecture 41 Play Video 
Proofs of the Great and Little Picard Theorems

Lecture 42 Play Video 
Royden's Theorem on Normality Based On Growth Of Derivatives

Lecture 43 Play Video 
Schottky's Theorem: Uniform Boundedness from a Point to a Neighbourhood
