This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes.

András Bátkai was born in Budapest, Hungary, in 1972, received his PhD in 2000 in Tübingen and is currently associate professor of mathematics at the Eötvös Loránd University Budapest. He is mainly interested in the theory and applications of operator semigroup theory, in paricular in applications to delay equations.He is the author of a research monograph and over 25 research papers, and the editor of the Open Mathematics journal. He was a fellow of the Alexander-von Humboldt Stiftung, held several Marie-Curie postdoctoral fellowships and and the Alexits prize of the Hungarian Academy of Sciences.

Marjeta Kramar Fijavz was born in 1973 in Ljubljana, Slovenia. She received her PhD in Mathematics in 2004 at University of Ljubljana and has been associate professor of mathematics there since 2013. Her primary interest is in linear algebra and operator theory, in particular operator semigroups, evolution equations, and dynamical networks.

Abdelaziz Rhandi was born in Casablanca, Morocco, in 1964. He received the first Ph.D degree from the University of Besançon (France) and the second Ph.D degree from the University of Tübingen (Germany). Presently, he is full professor of analysis at the University of Salerno (Italy). His main interest is in applied functional analysis and partial differential equations. He is the author of more than 50 publications, and the editor of the journals Semigroup Forum and Positivity. He was the winner of the 2006 HP Technology for Teaching Higher Education and a fellow of the Alexander-von Humboldt Stiftung.

1 An Invitation to Positive Matrices.- 2 Functional Calculus.- 3 Powers of Matrices.- 4 Matrix Exponential Function.- 5 Positive Matrices.- 6 Applications of Positive Matrices.- 7 Positive Matrix Semigroups and Applications.- 8 Positive Linear Systems.- 9 Banach Lattices.- 10 Positive Operators.- 11 Operator Semigroups.- 12 Generation Properties.- 13 Spectral Theory for Positive Semigroups I.- 14 Spectral Theory for Positive Semigroups II.- 15 An application to linear transport equations.- Appendices.- Index.