Part I Asteroseismology of red giants -- Aspects of observational red giant population seismology -- Asteroseismology of red giants as a tool for studying stellar populations: first steps -- Adiabatic solar-like oscillations in red giant stars -- Energetic aspects of non-radial solar-like oscillations in red giants -- Part II Internal structure, atmosphere, and evolution of red giants: current models and their uncertainties -- Evolution and internal structure of red giants -- Uncertainties and systematics in stellar evolution models of Red Giant Stars -- Convection modelling and the morphology of RGBs in stellar clusters -- Helium burning in moderate-mass stars -- Hydrodynamic simulations of shell convection in stellar cores -- Impact of rotational mixing on the global and asteroseismic properties of red giants -- 3D picture of the convective envelope of a rotating RGB star -- Effects of rotation and thermohaline mixing in red giant stars -- 3D Model Atmospheres of Red Giant Stars -- Part III Stellar populations in the Milky Way -- Structure and Evolution of the Milky Way -- Red Giant stars: probing the MilkyWay chemical enrichment -- Chemical abundances of giants in globular clusters -- TRILEGAL, a TRIdimensional modeL of thE GALaxy: status and future -- The Besanc¸on model of stellar population synthesis of the Galaxy.

Exciting results are blooming, thanks to a convergence between unprecedented asteroseismic data obtained by the satellites CoRoT and KEPLER, and state-of-the-art models of the internal structure of red giants and of galactic evolution. The pulsation properties now available for thousands of red giants promise to add valuable and independent constraints to current models of structure and evolution of our galaxy. Such a close connection between these domains opens a new very promising gate in our understanding of stars and galaxies. In this book international leaders in the field offer a wide perspective of the recent advancements in: Asteroseismology of red giants Models of the atmosphere, internal structure, and evolution of red giants Stellar population synthesis and models of the Milky Way