This book, "One-parameter Semigroups of Positive Operators," edited by Rainer Nagel and published by Springer-Verlag, is a comprehensive treatise on the theory of one-parameter semigroups of positive linear operators. The book is structured into four main parts: Part A focuses on semigroups on Banach spaces, Part B on semigroups on spaces \(C_0(X)\), Part C on semigroups on Banach lattices, and Part D on semigroups on C*- and W*-algebras. Each part is divided into sections covering basic results, characterization, spectral theory, and asymptotic behavior. The authors, including Wolfgang Arendt, Annette Grabosch, Günther Greiner, Ulrich Moustakas, Rainer Nagel, Ulf Schlotterbeck, Ulrich Groh, Heinrich P. Lotz, and Frank Neubrander, contribute to these sections, providing detailed insights into the theory and applications of positive semigroups in various mathematical contexts. The book aims to integrate the functional analytic theory with the study of Cauchy problems and to address the gaps in the original ties with applications, particularly in probability theory, partial differential equations, transport theory, mathematical biology, and physics.This book, "One-parameter Semigroups of Positive Operators," edited by Rainer Nagel and published by Springer-Verlag, is a comprehensive treatise on the theory of one-parameter semigroups of positive linear operators. The book is structured into four main parts: Part A focuses on semigroups on Banach spaces, Part B on semigroups on spaces \(C_0(X)\), Part C on semigroups on Banach lattices, and Part D on semigroups on C*- and W*-algebras. Each part is divided into sections covering basic results, characterization, spectral theory, and asymptotic behavior. The authors, including Wolfgang Arendt, Annette Grabosch, Günther Greiner, Ulrich Moustakas, Rainer Nagel, Ulf Schlotterbeck, Ulrich Groh, Heinrich P. Lotz, and Frank Neubrander, contribute to these sections, providing detailed insights into the theory and applications of positive semigroups in various mathematical contexts. The book aims to integrate the functional analytic theory with the study of Cauchy problems and to address the gaps in the original ties with applications, particularly in probability theory, partial differential equations, transport theory, mathematical biology, and physics.