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The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, thus providing the complex analysis backbone of Loewner theory. The new materials found in this edition give a concise and accessible treatment of Loewner theory. Some of them have been described in research papers only or appear here for the first time. Each chapter finishes with exercises.

The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, thus providing the complex analysis backbone of Loewner theory. The new materials found in this edition give a concise and accessible treatment of Loewner theory. Some of them have been described in research papers only or appear here for the first time. Each chapter finishes with exercises.