Presenting Fourier series from the aspect of several variables, this book covers connections between Fourier analysis and partial differential equations. It discusses newly emerging topics, such as the fundamental results on Calderon-Zygmund kernels in multi-dimensions and their relation to Fourier series and integrals, along with Fourier integrals and their applications to uniqueness for two-dimensional trigonometric series. The author explores important applications for the first time through reaction-diffusion equations and Navier-Stokes equations. The text also covers spherical harmonics...