This chapter covers the application of Fourier analysis in solving differential and integral equations, emphasizing its vital role in mathematical physics and engineering. The chapter systematically demonstrates how Fourier transforms can effectively solve ordinary differential equations (ODEs) through various methods and examples. Building on this foundation, the discussion transitions to integral equations, where Fourier transforms offer powerful techniques for tackling complex integral problems. The chapter further addresses partial differential equations (PDEs), introducing essential concepts such as the principle of superposition and the variable separation method, which are crucial for effective PDE solutions. Specific examples are presented, including detailed analyses of the one-dimensional and two-dimensional heat equations and the one-dimensional wave equation. The exploration of the two-dimensional Laplace equation with boundary conditions highlights the practical applications of Fourier analysis in addressing real-world issues. Finally, the chapter discusses the classification of partial differential equations, providing insights into their diverse nature and solutions. Through this thorough exploration, the chapter reinforces the significance of Fourier analysis in enhancing the understanding and resolution of differential and integral equations.