This chapter covers the mathematical theory of how plane waves are reflected by boundaries or interfaces separating solid layers in the subsurface and how they are transmitted through them. Reflections off the Earth's surface are also discussed. The equations describing the physical boundary conditions that incident, reflected, and transmitted waves must satisfy are derived. The calculation of reflection and transmission coefficients, which give the amplitudes of reflected and transmitted waves, is covered.Polarity reversals and phase changes are discussed. Critical angles, which are related to the total internal reflection of incident waves, are studied. This is followed by coverage of the calculation of the amount of seismic wave energy that is reflected and transmitted, reflection and transmission of waves from liquid–liquid, liquid–solid, and rigid boundaries, and approximate formulas for reflection and transmission coefficients.