soon recognized that its mass is very close to the combined mass of the D 0 and ¯ D 0 ∗ mesons. For this reason the X (3872) has been widely interpreted as a loosely bound D 0 ¯ D 0 ∗ molecular state [37, 124, 113, 123, 9, 122, 80, 75]. Another interpretation is that the X (3872) is a tetraquark, and is expected to be only one member of a nonet of tetraquarks [84, 44, 86, 121, 43]. Quite recently, the Z ± c (3895) was discovered by the BES-III collaboration [6] and confirmed by the Belle [81] and CLEO collaborations [128]. Because charmonium states cannot be electrically charged, this state cannot be a charmonium state. Like the X (3872), the Z ± c (3895) decays to J/ψ , hence it must contain ¯ cc . However, this combination cannot produce an electric charge. The simplest explanation for this state is that it is a four-quark state of the form c ¯ cq$_{i}$ ¯ q$_{j}$ , where q$_{i}$ and ¯ q$_{j}$ are light quarks with different flavours. In fact, Ref. [84] predicted the existence of the Z ± c (3895) on the basis of a tetraquark model of the X (3872). The X (3872) and Z ± c (3895) are discussed in Chapter 4. Quantum Chromodynamics (QCD) is the fundamental theory of strong interactions. It is a quantum field theory, which is a generalization of quantum mechanics to describe physical processes involving particle creation or annihilation. It is important to stress that quantum mechanics is incapable of this: the wave function of a particle that has not yet been created or has been annihilated cannot be normalized, and thus is incompatible with the statistical interpretation of quantum mechanics. In quantum field theory particles are understood as being excitations, or quanta, of quantum fields. There are two distinct approaches that are used to construct a quantum field theory. Canonical quantization involves reinterpreting classical fields as operators that satisfy a certain algebra. A second approach utilizes the path integral formulation of quantum mechanics (see Ref. [50] for a review). Both methods will be utilized in this chapter to formulate QCD. 1.3 Quantum Chromodynamics 10