This chapter covers higher-dimensional Fourier analysis, broadening the principles of Fourier transforms into multiple dimensions. It begins with a clear introduction to fundamental concepts and then delves into the distinctive properties and mathematical framework of the multidimensional Fourier transform. The discussion includes the Fourier transform of separable functions, simplifying the analysis of complex multivariable systems by breaking them into manageable components. Additionally, the chapter examines radial functions in two dimensions, highlighting the importance of symmetry in higher-dimensional spaces. It also discusses higher-dimensional impulse responses, illustrating their significance in signal processing and system analysis when exposed to multidimensional stimuli. Finally, the chapter covers the principles of higher-dimensional sampling, which is vital for accurately capturing and reconstructing signals across multiple dimensions. By integrating these concepts, this chapter offers a thorough understanding of how higher-dimensional Fourier analysis enhances the analysis and processing of multivariable data, making it invaluable for various applications in engineering, physics, and applied mathematics.