Ioannis Emmanouil was initiated to mathematics in Athens, Greece and then moved to Berkeley, where he studied homological algebra, algebraic geometry and K-theory with Mariusz Wodzicki. After receiving his Ph.D. from Berkeley in 1994, he taught for three years at the University of Michigan as a Hildebrandt Assistant Professor. He moved back to Europe in 1997 and after a year at IHES, returned to Greece in 1998. At present, he is a member of the faculty of the University of Athens.

From the reviews: "The study of idempotent elements in the group algebras originates from geometric and analytic considerations. ... This book provides an introduction to the study of these problems for graduate students and researchers ... . collects and presents in a systematic way basic techniques and important results that have been obtained during the past few decades. ... The book is suitable for independent study ... . Moreover, all chapters and appendices finish with a sufficient number of exercises that also increase the quality of the book." (S. V. Mihovski, Zentralblatt MATH, Vol. 1093 (19), 2006)

• Introduction.- Motivating Examples.- Reduction to Positive Characteristic.- A Homological Approach.- Completions of CG.- Appendices: Tools from Commutative Algebra.- Discrete Ring-valued Integrals.- Frobenius' Density Theorem.- Homological Techniques.- Comparison of Projections.

Ioannis Emmanouil was initiated to mathematics in Athens, Greece and then moved to Berkeley, where he studied homological algebra, algebraic geometry and K-theory with Mariusz Wodzicki. After receiving his Ph.D. from Berkeley in 1994, he taught for three years at the University of Michigan as a Hildebrandt Assistant Professor. He moved back to Europe in 1997 and after a year at IHES, returned to Greece in 1998. At present, he is a member of the faculty of the University of Athens.

From the reviews: "The study of idempotent elements in the group algebras originates from geometric and analytic considerations. ... This book provides an introduction to the study of these problems for graduate students and researchers ... . collects and presents in a systematic way basic techniques and important results that have been obtained during the past few decades. ... The book is suitable for independent study ... . Moreover, all chapters and appendices finish with a sufficient number of exercises that also increase the quality of the book." (S. V. Mihovski, Zentralblatt MATH, Vol. 1093 (19), 2006)

• Introduction.- Motivating Examples.- Reduction to Positive Characteristic.- A Homological Approach.- Completions of CG.- Appendices: Tools from Commutative Algebra.- Discrete Ring-valued Integrals.- Frobenius' Density Theorem.- Homological Techniques.- Comparison of Projections.

Ioannis Emmanouil was initiated to mathematics in Athens, Greece and then moved to Berkeley, where he studied homological algebra, algebraic geometry and K-theory with Mariusz Wodzicki. After receiving his Ph.D. from Berkeley in 1994, he taught for three years at the University of Michigan as a Hildebrandt Assistant Professor. He moved back to Europe in 1997 and after a year at IHES, returned to Greece in 1998. At present, he is a member of the faculty of the University of Athens.

From the reviews: "The study of idempotent elements in the group algebras originates from geometric and analytic considerations. ... This book provides an introduction to the study of these problems for graduate students and researchers ... . collects and presents in a systematic way basic techniques and important results that have been obtained during the past few decades. ... The book is suitable for independent study ... . Moreover, all chapters and appendices finish with a sufficient number of exercises that also increase the quality of the book." (S. V. Mihovski, Zentralblatt MATH, Vol. 1093 (19), 2006)

• Introduction.- Motivating Examples.- Reduction to Positive Characteristic.- A Homological Approach.- Completions of CG.- Appendices: Tools from Commutative Algebra.- Discrete Ring-valued Integrals.- Frobenius' Density Theorem.- Homological Techniques.- Comparison of Projections.