This book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas: one in complex analysis and one in number theory, it has been discovered that a number of striking similarities exist between these two subjects. A growing understanding of these connections has led to significant advances in both fields. Outstanding conjectures from decades ago are being solved. Over the past 20 years since the first edition appeared, there have been many new and significant developments. The new edition greatly expands the materials. In addition, three new chapters were added. In particular, the theory of algebraic curves, as well as the algebraic hyperbolicity, which provided the motivation for the Nevanlinna theory. Key Features: o Uniquely combined Nevanlinna theory and Diophantine approximation together in the book. Each chapter was divided into Part A and Part B. The Part A deals with Nevanlinna theory and Part B covers Diophantine approximation. At the end of each chapter, a table is provided to indicate the clear correspondence of the theorems o In the Chapter 7 "Extension of Cartan’s theorem and Schmidt’s subspace theorem" of this book, the recent development of the "filtration method" was presented in a systematic way. It appeared the first time in the existing literatures o There have been a great research activities in the study of complex hyperbolicities. Various conjectures have been solved. This book contains the most updated materials about the research in this direction

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