1: Holomorphic Functions in Several Variables — Read

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1.1: Onto Several Variables
1.2: Power Series Representation
1.3: Derivatives
1.4: Inequivalence of Ball and Polydisc
1.5: Cartan's Uniqueness Theorem
Cartan's uniqueness theorem is another analogue of Schwarz’s lemma to several variables. It says that for a bounded domain, it is enough to know that a self mapping is the identity at a single point to show that it is the identity everywhere. As there are quite a few theorems named for Cartan, this one is often referred to as the Cartan's uniqueness theorem. It is useful in computing the automorphism groups of certain domains.
1.6: Riemann Extension Theorem, Zero Sets, and Injective Maps

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