Introduction. The second part of the book is dedicated to the dressed atom, and it begins with this chapter, which deals mainly with the quantum-dynamical description of an atom dressed by a real electro-magnetic field. Here the emphasis is on the adjective ‘real’, by which we mean that the field is in an excited state populated by real photons and not just by the zero-point photon background. Due to the coupling discussed in the first part of the book, atom-photon correlations are established which admix, shift and split the levels of the system atom plus radiation field. The admixed and correlated states are called dressed-atom states. In Section 5.2 we obtain the Hamiltonian for an atom in a cavity with perfectly reflecting walls. The cavity selects a discrete set of field modes, and this leads us naturally to consider the simplest possible nontrivial atom-field system: the Jaynes-Cummings model describing a two-level atom coupled to a single-mode system. In Section 5.3 we develop the theory, based on a unitary transformation, to dress a two-level atom by a mode of the cavity populated by real photons. A necessary preliminary for dealing with more complicated atom-field models is the theory of spontaneous emission in free space, which is discussed in Section 5.4 in a Wigner-Weisskopf framework.