From the reviews: "In the monograph under review, designed as a textbook for graduate students, the author aims to build up the theory in a straightforward way in view of physical applications. ... The material covered in the book was used in a two-semester course for graduate students. The book is a good summary of the most important facts of the theory of evolution equations, and is also a good source of information for researchers looking for new applications of this theory." (Andras Batkai, Mathematical Reviews, Issue 2008 h) "This well-written work is the outgrowth of a two-semester course on linear semigroup methods, linear and quasi-linear hyperbolic systems of partial differential equations, and the abstract theory of evolution equations ... . Although the text was written for truly advanced graduate students, it contains a wealth of well presented results on semigroup theory of evolution equations ... and will therefore serve as a valuable resource for researchers in mathematics and theoretical physics as well." (Thomas Hagen, Zentralblatt MATH, Vol. 1144, 2008)

• Conventions.- Mathematical Introduction.- Prerequisites.- Strongly Continuous Semigroups.- Examples of Generators of Strongly Continuous Semigroups.- Intertwining Relations, Operator Homomorphisms.- Examples of Constrained Systems.- Kernels, Chains, and Evolution Operators.- The Linear Evolution Equation.- Examples of Linear Evolution Equations.- The Quasi-Linear Evolution Equation.- Examples of Quasi-Linear Evolution Equations.

From the reviews: "In the monograph under review, designed as a textbook for graduate students, the author aims to build up the theory in a straightforward way in view of physical applications. ... The material covered in the book was used in a two-semester course for graduate students. The book is a good summary of the most important facts of the theory of evolution equations, and is also a good source of information for researchers looking for new applications of this theory." (Andras Batkai, Mathematical Reviews, Issue 2008 h) "This well-written work is the outgrowth of a two-semester course on linear semigroup methods, linear and quasi-linear hyperbolic systems of partial differential equations, and the abstract theory of evolution equations ... . Although the text was written for truly advanced graduate students, it contains a wealth of well presented results on semigroup theory of evolution equations ... and will therefore serve as a valuable resource for researchers in mathematics and theoretical physics as well." (Thomas Hagen, Zentralblatt MATH, Vol. 1144, 2008)

• Conventions.- Mathematical Introduction.- Prerequisites.- Strongly Continuous Semigroups.- Examples of Generators of Strongly Continuous Semigroups.- Intertwining Relations, Operator Homomorphisms.- Examples of Constrained Systems.- Kernels, Chains, and Evolution Operators.- The Linear Evolution Equation.- Examples of Linear Evolution Equations.- The Quasi-Linear Evolution Equation.- Examples of Quasi-Linear Evolution Equations.

From the reviews: "In the monograph under review, designed as a textbook for graduate students, the author aims to build up the theory in a straightforward way in view of physical applications. ... The material covered in the book was used in a two-semester course for graduate students. The book is a good summary of the most important facts of the theory of evolution equations, and is also a good source of information for researchers looking for new applications of this theory." (Andras Batkai, Mathematical Reviews, Issue 2008 h) "This well-written work is the outgrowth of a two-semester course on linear semigroup methods, linear and quasi-linear hyperbolic systems of partial differential equations, and the abstract theory of evolution equations ... . Although the text was written for truly advanced graduate students, it contains a wealth of well presented results on semigroup theory of evolution equations ... and will therefore serve as a valuable resource for researchers in mathematics and theoretical physics as well." (Thomas Hagen, Zentralblatt MATH, Vol. 1144, 2008)

• Conventions.- Mathematical Introduction.- Prerequisites.- Strongly Continuous Semigroups.- Examples of Generators of Strongly Continuous Semigroups.- Intertwining Relations, Operator Homomorphisms.- Examples of Constrained Systems.- Kernels, Chains, and Evolution Operators.- The Linear Evolution Equation.- Examples of Linear Evolution Equations.- The Quasi-Linear Evolution Equation.- Examples of Quasi-Linear Evolution Equations.