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First we shall present some basic facts about condenser capacity, Green functions and their relation with Complex Analysis. We will give an inequality for condenser capacity under holomorphic functions, depending on the valency of the holomorphic function on the positive plate of the condenser. Finally, we will examine the asymptotic behavior of the capacity of the inverse image of a condenser under exponential Blaschke products and universal covering maps. (Based on joint works with M. Papadimitrakis and J. Mashreghi.)