1. Approximation of Algebraic Numbers.- 2. Effective Constructions in Transcendental Number Theory.- 3. Hilbert's Seventh Problem.- 4. Multidimensional Generalization of Hilbert's Seventh Problem.- 5. Values of Analytic Functions That Satisfy Linear Differential Equations.- 6. Algebraic Independence of the Values of Analytic Functions That Have an Addition Law.

This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.