Standard courses in complex analysis do not guide students to choose this seemingly closed subject as their research topic. However, this book presents one part of modern complex analysis: geometric function theory, not as a closed subject but instead as a fruitful synthesis of many different areas: functional analysis, invariant geometry, harmonic analysis, differential geometry, partial differential equations, the automorphism groups of domains and abstract algebra. It will capture the imagination of advanced undergraduate and graduate students and other mathematicians and it shows how to formulate problems. Moreover, the book is nicely-written, readable and a methodologically designed showroom of modern mathematics. It contains many exercises, examples and an extensive bibliography. The statement, “There is hardly any other analysis text that offers such a variety and synthesis of mathematical topics”, (cited from the preface) is not exaggerated. The book will be useful for a wide range of students and mathematicians.