This chapter presents in detail the basic theory of Fourier analysis for the continuous-time domain. More specifically, the defining equations of the trigonometric and exponential Fourier expansion for the case of periodic continuous-time signals are derived, together with the convergence conditions and associated properties. The chapter presents interesting aspects of Fourier analysis, such as the Gibbs phenomenon, Parseval’s theorem, and the effect of a linear time-invariant system on each frequency component of a continuous-time input signal. The focus then shifts to the Fourier transform of general aperiodic signals. Its defining equation is derived and the transformation of the line spectrum of periodic signals to the continuous spectrum of aperiodic signals is described in detail, together with the convergence conditions of the Fourier transform. A set of representative examples is given to help readers understand the process of its calculation. The properties of the Fourier transform are then proven and used to simplify its calculation, the Fourier transform of periodic signals and the inverse Fourier transform are described, and the very important bandwidth theorem is presented. The chapter concludes with a description of continuous-time systems in the frequency domain (amplitude/phase representation, convolution theorem, and linear and nonlinear phase systems), and a first reference is made to ideal and real (nonideal) frequency selective filters.