This chapter extends from the Fourier series to a broader framework in Fourier analysis. It begins by introducing the Fourier integral, which generalizes the Fourier series to accommodate non-periodic functions, broadening the applicability of Fourier methods to a wider range of signals. The chapter then delves into the properties of the Fourier transform, the core element of Fourier analysis, and examines essential features such as transform pair duality, linearity, constant multiplication, and symmetry. These properties enable critical manipulations for signal processing. Additionally, topics such as frequency shifts, scaling, and the differentiation of Fourier pairs provide greater flexibility for analyzing complex signals. These properties make the Fourier transform an invaluable tool across physics, engineering, and applied sciences. This chapter establishes a solid foundation in Fourier analysis, preparing readers for more advanced techniques in signal transformation and analysis.