John B. Garnett is Professor of Mathematics in the Department of Mathematics at University of California, Los Angeles. Donald E. Marshall is Professor of Mathematics in the Department of Mathematics at University of Washington, Seattle.

• 1. Jordan domains; 2. Finitely connected domains; 3. Potential theory; 4. Extremal distance; 5. Applications and reverse inequalities; 6. Simply connected domains, part one; 7. Bloch functions and quasicircles; 8. Simply connected domains, part two; 9. Infinitely connected domains; 10. Rectifiability and quadratic expressions; Appendices.

'The authors say that they wrote this book to explain the exciting new developments in the subject over the past couple of decades. They have achieved this with an impressive scholarship and outstanding expository clarity. … it has clearly been written with great care and deep insight into the subject matter. I expect it to become a highly valued addition to the bookshelves of students and experienced researchers alike.' Zentralblatt MATH

John B. Garnett is Professor of Mathematics in the Department of Mathematics at University of California, Los Angeles. Donald E. Marshall is Professor of Mathematics in the Department of Mathematics at University of Washington, Seattle.

• 1. Jordan domains; 2. Finitely connected domains; 3. Potential theory; 4. Extremal distance; 5. Applications and reverse inequalities; 6. Simply connected domains, part one; 7. Bloch functions and quasicircles; 8. Simply connected domains, part two; 9. Infinitely connected domains; 10. Rectifiability and quadratic expressions; Appendices.

'The authors say that they wrote this book to explain the exciting new developments in the subject over the past couple of decades. They have achieved this with an impressive scholarship and outstanding expository clarity. … it has clearly been written with great care and deep insight into the subject matter. I expect it to become a highly valued addition to the bookshelves of students and experienced researchers alike.' Zentralblatt MATH

John B. Garnett is Professor of Mathematics in the Department of Mathematics at University of California, Los Angeles. Donald E. Marshall is Professor of Mathematics in the Department of Mathematics at University of Washington, Seattle.

• 1. Jordan domains; 2. Finitely connected domains; 3. Potential theory; 4. Extremal distance; 5. Applications and reverse inequalities; 6. Simply connected domains, part one; 7. Bloch functions and quasicircles; 8. Simply connected domains, part two; 9. Infinitely connected domains; 10. Rectifiability and quadratic expressions; Appendices.

'The authors say that they wrote this book to explain the exciting new developments in the subject over the past couple of decades. They have achieved this with an impressive scholarship and outstanding expository clarity. … it has clearly been written with great care and deep insight into the subject matter. I expect it to become a highly valued addition to the bookshelves of students and experienced researchers alike.' Zentralblatt MATH