This book deals with models and model-building in classical and quantum physics it relies on
logic and the philosophy of science as well as on modern mathematics. The reader will also find
vistas into the history of ideas. The philosophical analysis is based on the separation of
syntax and semantics which is at the root of Kolmogorov's theory of probability recursive
functions and algorithmic complexity are used to discuss entropy and randomness. Basic concepts
are discussed together with concrete physical models for phase transitions scaling
renormalization semigroups and the irreversible approach to equilibrium. The book is intended
for mathematicians physicists and philosophers of science both researchers and graduate
students.
