Introduction: Nonlinear Waves -- Brief History and Overview of Nonlinear Water Waves -- Nonlinear Water Wave Equations -- Infinite-Line Inverse Scattering Transform -- Infinite-Line Hirota Method -- Periodic Boundary Conditions -- Periodic Boundary Conditions: Physics, Data Analysis, Data Assimilation, and Modeling -- Periodic Hirota Method -- Multidimensional Fourier Analysis -- Multidimensional Fourier Series -- Riemann Theta Functions -- Riemann Theta Functions as Ordinary Fourier Series -- Nonlinear Shallow-Water Spectral Theory -- Periodic Korteweg-DeVries Equation -- Periodic Kadomtsev-Petviashvili Equation -- Nonlinear Deep-Water Spectral Theory -- Periodic Nonlinear Schrodinger Equation -- Hilbert Transform --

Nonlinear Fourier Analysis and Filtering of Ocean Waves -- Laboratory Experiments of Rogue Waves -- Nonlinearity in Duck Pier Data -- Harmonic Generation in Shallow-Water Waves -- Nonlinear Hyperfast Numerical Modeling -- Hyperfast Modeling of Shallow-Water Waves: The KdV and KP Equations -- Modeling the 2 + 1 Gardner Equation -- Modeling the Davey-Stewartson (DS) Equations.