The course Spectral Analysis of nonlinear Waves in the Coastal Area imparts an overview of linear and nonlinear wave theories. The cnoidal wave theory is put into focus and described with the help of the theta-function. Different analysis methods like the Hilbert-Huang transformation as well as the linear and nonlinear Fourier transform are presented and their advantages and disadvantages are discussed. Finally, the methods are applied to different examples of surface waves and different problems in coastal engineering.