In this paper, we introduce the foundations of the Statistical Wave Field Theory. This theory establishes the statistical laws of waves propagating in a closed bounded volume, that are mathematically implied by the boundary-value problem of the wave equation. These laws are derived from the Sturm-Liouville theory and the mathematical theory of dynamical billiards. They hold after many reflections on the boundary surface, and at high frequency. This is the first statistical theory of reverberation which provides the closed-form expression of the power distribution and the correlations of the wave field jointly over time, frequency, and space inside the bounded volume, in terms of the geometry and the specific admittance of its boundary surface. The Statistical Wave Field Theory may find applications in various science fields, including room acoustics, electromagnetic theory, and nuclear physics.