Interstellar dust grains catalyse chemical reactions, absorb, scatter, polarise and re-radiate starlight and constitute the building blocks for the formation of planets. Understanding this interstellar component is therefore of primary importance in many areas of astronomy & astrophysics. For example, observers need to understand how dust effects light passing through molecular clouds. Astrophysicists wish to comprehend how dust enables the collapse of clouds or how it determines the spectral behaviour of protostars, star forming regions or whole galaxies. This book gives a thorough theoretical description of the fundamental physics of interstellar dust - its composition, morphology, size distribution, dynamics, optical and thermal properties, alignment, polarisation, scattering, radiation and spectral features. This encyclopaedic book provides the basic physics towards understanding the solid matter in interstellar space. It includes all the necessary physics, including solid state physics, radiative transport, optical properties, thermodynamics, statistical mechanics and quantum mechanics. It then uses all of this basic physics in the specific case of dust grains in the interstellar medium. Interstellar dust clouds catalyse simple chemical reactions, absorbs, scatters, polarises and re-radiates starlight and forms the building blocks for planet and stellar formation. Understanding this interstellar medium is then of primary importance in many areas of astronomy & astrophysics. For example observers need to understand how it effects light passing through dust and molecular clouds, astrophysicists need to comprehend the formation and structure of dust clouds and how it collapses to form stars and planets. Written in an accessible and descriptive manner, this will be essential supplementary reading for advanced undergraduate and graduate students taking courses on the interstellar medium and active researchers in need of a single source of well illustrated and detailed information.