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.
Contents:

The Theory of Algebraic Curves

The First Main Theorem and the Theory of Height

Nevanlinna Theory for Meromorphic Functions and Roth's Theorem

Holomorphic Curves into Compact Riemann Surfaces

Holomorphic Curves in Pn(C) and Schmidt's Subspace Theorem

The Moving Target Problems

Extension of Cartan's Theorem and Schmidt's Subspace Theorem

Equi-dimensional Nevanlinna Theory and Vojta's Conjecture

Holomorphic Curves in Abelian Varieties and the Theorem of Faltings

Complex Hyperbolic Manifolds and Lang's Conjecture

Readership: Researchers and graduate students in the area of complex analysis (including several complex variables and complex geometry), number theory, algebraic/differential geometry.