This paper presents solutions to Maxwell's equations in nonlinear dielectrics that satisfy boundary conditions at a plane interface between a linear and nonlinear medium. It generalizes the laws of reflection and refraction for harmonic waves at the boundary, and derives generalizations of the Fresnel formulas for intensity and polarization conditions. The equivalent Brewster angle for harmonic waves is derived, and the conditions for total reflection and transmission of boundary harmonics are discussed. The solution of the nonlinear plane parallel slab is presented, which describes harmonic generation in experimental situations. An integral equation formulation for wave propagation in nonlinear media is sketched. The implications of the nonlinear boundary theory for experimental systems and devices are pointed out. The paper discusses the general laws of reflection and refraction for harmonic waves at the boundary of a nonlinear medium. It shows that the inhomogeneous source wave, the homogeneous transmitted and reflected waves at the sum frequency, and the boundary normal all lie in the same plane. The propagation of the inhomogeneous wave at the sum frequency is given by an exponential function. The wave vectors of the refracted waves are determined by Snell's law. The paper also discusses the polarization and intensities of the harmonic waves, showing that the reflected wave is out of phase with the nonlinear polarization. The transmitted wave starts with an intensity of about the same magnitude and grows as the destructive interference between the homogeneous and inhomogeneous solutions diminishes. The total power flow is conserved because the fundamental wave will have reflected and transmitted intensities slightly less than in the case of a strictly linear dielectric. The paper also discusses the generalization of the laws of reflection and refraction for harmonic waves at the boundary of a nonlinear medium. It shows that the inhomogeneous source wave, the homogeneous transmitted and reflected waves at the sum frequency, and the boundary normal all lie in the same plane. The propagation of the inhomogeneous wave at the sum frequency is given by an exponential function. The wave vectors of the refracted waves are determined by Snell's law. The paper also discusses the polarization and intensities of the harmonic waves, showing that the reflected wave is out of phase with the nonlinear polarization. The transmitted wave starts with an intensity of about the same magnitude and grows as the destructive interference between the homogeneous and inhomogeneous solutions diminishes. The total power flow is conserved because the fundamental wave will have reflected and transmitted intensities slightly less than in the case of a strictly linear dielectric.This paper presents solutions to Maxwell's equations in nonlinear dielectrics that satisfy boundary conditions at a plane interface between a linear and nonlinear medium. It generalizes the laws of reflection and refraction for harmonic waves at the boundary, and derives generalizations of the Fresnel formulas for intensity and polarization conditions. The equivalent Brewster angle for harmonic waves is derived, and the conditions for total reflection and transmission of boundary harmonics are discussed. The solution of the nonlinear plane parallel slab is presented, which describes harmonic generation in experimental situations. An integral equation formulation for wave propagation in nonlinear media is sketched. The implications of the nonlinear boundary theory for experimental systems and devices are pointed out. The paper discusses the general laws of reflection and refraction for harmonic waves at the boundary of a nonlinear medium. It shows that the inhomogeneous source wave, the homogeneous transmitted and reflected waves at the sum frequency, and the boundary normal all lie in the same plane. The propagation of the inhomogeneous wave at the sum frequency is given by an exponential function. The wave vectors of the refracted waves are determined by Snell's law. The paper also discusses the polarization and intensities of the harmonic waves, showing that the reflected wave is out of phase with the nonlinear polarization. The transmitted wave starts with an intensity of about the same magnitude and grows as the destructive interference between the homogeneous and inhomogeneous solutions diminishes. The total power flow is conserved because the fundamental wave will have reflected and transmitted intensities slightly less than in the case of a strictly linear dielectric. The paper also discusses the generalization of the laws of reflection and refraction for harmonic waves at the boundary of a nonlinear medium. It shows that the inhomogeneous source wave, the homogeneous transmitted and reflected waves at the sum frequency, and the boundary normal all lie in the same plane. The propagation of the inhomogeneous wave at the sum frequency is given by an exponential function. The wave vectors of the refracted waves are determined by Snell's law. The paper also discusses the polarization and intensities of the harmonic waves, showing that the reflected wave is out of phase with the nonlinear polarization. The transmitted wave starts with an intensity of about the same magnitude and grows as the destructive interference between the homogeneous and inhomogeneous solutions diminishes. The total power flow is conserved because the fundamental wave will have reflected and transmitted intensities slightly less than in the case of a strictly linear dielectric.