Understandingnon-equilibrium properties of classical and quantum many-particle systems is oneof the goals of contemporary statistical mechanics. Besides its own interestfor the theoretical foundations of irreversible thermodynamics(e.g. of theFourier's law of heat conduction), this topic is also relevant to developinnovative ideas for nanoscale thermal management with possible future applicationsto nanotechnologies and effective energetic resources.The first part of thevolume (Chapters 1-6) describes the basic models, the phenomenology and thevarious theoretical approaches to understand heat transport in low-dimensionallattices (1D e 2D). The methods described will include equilibrium and nonequilibriummolecular dynamics simulations, hydrodynamic and kinetic approaches and thesolution of stochastic models.The second part(Chapters 7-10) deals with applications to nano and microscale heat transfer,as for instance phononic transport in carbon-based nanomaterials, including theprominent case of nanotubes and graphene. Possible future developments  onheat flow control and thermoelectric energy conversion will be outlined.This volume aims atbeing the first step for graduate students and researchers entering the fieldas well as a reference for the community of scientists that, from differentbackgrounds (theoretical physics, mathematics, material sciences andengineering), has grown in the recent years around those themes.

Understandingnon-equilibrium properties of classical and quantum many-particle systems is oneof the goals of contemporary statistical mechanics. Besides its own interestfor the theoretical foundations of irreversible thermodynamics(e.g. of theFourier's law of heat conduction), this topic is also relevant to developinnovative ideas for nanoscale thermal management with possible future applicationsto nanotechnologies and effective energetic resources.The first part of thevolume (Chapters 1-6) describes the basic models, the phenomenology and thevarious theoretical approaches to understand heat transport in low-dimensionallattices (1D e 2D). The methods described will include equilibrium and nonequilibriummolecular dynamics simulations, hydrodynamic and kinetic approaches and thesolution of stochastic models.The second part(Chapters 7-10) deals with applications to nano and microscale heat transfer,as for instance phononic transport in carbon-based nanomaterials, including theprominent case of nanotubes and graphene. Possible future developments  onheat flow control and thermoelectric energy conversion will be outlined.This volume aims atbeing the first step for graduate students and researchers entering the fieldas well as a reference for the community of scientists that, from differentbackgrounds (theoretical physics, mathematics, material sciences andengineering), has grown in the recent years around those themes.