The book builds upon the lecture notes of an undergraduate course in Astronomical Spectroscopy, but contains significant material for post-graduate courses. It describes the basic physical principles of atomic spectroscopy and the absorption and emission of radiation in astrophysical and laboratory plasmas. It summarizes the basics of Electromagnetism and Thermodynamics, then describes in detail the theory of atomic spectra for complex atoms, with emphasis on astrophysical applications. Equilibrium and non-equilibrium phenomena in plasmas are considered. The interaction between radiation and matter is described, together with various types of radiation (e.g. cyclotron, syncrotron, bremsstrahlung, Compton). The basic theory of polarization is provided, as well as the theory of radiative transfer for astrophysical applications.