This book is an introduction to the theory of quasiregular mappings in real n-dimensional space, a new field of mathematical study that has emerged during the past 20 years. The exposition is self-contained and thus accessible to a wide readership. A broad spectrum of results of both analytic and geometric character are presented, and the methods vary accordingly. The main tools are the variational integral method and the extremal length method, both of which are thoroughly developed here. The author is noted as one of the developers of the theory of quasiregular mappings, particularly for his work in value distribution theory. Many of the topics treated here are published for the first time in book form.

Inhalt
I. Basic Properties of Quasiregular Mappings.- 1. ACLp Mappings.- 2. Quasiregular Mappings.- 3. Examples.- 4. Discrete Open Mappings.- II. Inequalities for Moduli of Path Families.- 1. Modulus of a Path Family.- 2. The KO-Inequality.- 3. Path Lifting.- 4. Linear Dilatations.- 5. Poletski?'s Lemma.- 6. Characterizations of Quasiregularity.- 7. Proof of Poletski?'s Lemma.- 8. Poletski?'s Inequality.- 9. Väisälä's Inequality.- 10. Capacity Inequalities.- III. Applications of Modulus Inequalities.- 1. Global Distortion.- 2. Sets of Capacity Zero and Singularities.- 3. The Injectivity Radius of a Local Homeomorphism.- 4. Local Distortion.- 5. Bounds for the Local Index.- IV. Mappings into the n-Sphere with Punctures.- 1. Coverings Averages.- 2. The Analogue of Picard's Theorem.- 3. Mappings of a Ball.- V. Value Distribution.- 1. Defect Relation.- 2. Coverings and Decomposition of Balls.- 3. Estimates on Liftings.- 4. Extremal Maximal Sequences of Liftings.- 5. Effect of the Defect Sum on the Liftings.- 6. Completion of the Proof of Defect Relations.- 7. Mappings of the Plane.- 8. Order of Growth.- 9. Further Results.- VI. Variational Integrals and Quasiregular Mappings.- 1. Extremals of Variational Integrals.- 2. Extremals and Quasiregular Mappings.- 3. Growth Estimates for Extremals.- 4. Differentiability of Quasiregular Mappings.- 5. Discreteness and Openness of Quasiregular Mappings.- 6. Pullbacks of General Kernels.- 7. Further Properties of Extremals.- 8. The Limit Theorem.- VII. Boundary Behavior.- 1. Removability.- 2. Asymptotic and Radial Limits.- 3. Continuity Results and the Reflection Principle.- 4. The Wiener Condition.- 5. F-Harmonic Measure.- 6. Phragmén-Lindelöf Type Theorems.- 7. Asymptotic Values.- List of Symbols.