Ch 1- Introduction
Ch 2- Hydrodynamic limits for independent particles
Ch 3- Hydrodynamics of the zero range process
Ch 4- Particle models for reaction-diffusion equations
Ch 5- Particle models for the Carleman equation
Ch 6- The Glauber+Kawasaki process
Ch 7- Hydrodynamic limits in kinetic models
Ch 8- Phase separation and interface dynamics
Ch 9- Escape from an unstable equilibrium
Ch 10- Estimates on the V-functions

Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models.