This Chapter is devoted to the analysis of sequential measurements of physical quantities, in which the “time” variable may be either continuous or discrete. Formal definitions and classifications of random variables and random processes precede the topics of the central limit theorem and stable distributions, both in the context of random walks and their asymptotic regimes. We discuss discrete-time and continuous-time Markov chains, and describe methods of generating noise with arbitrary spectral properties. Correlation and auto-correlation of signals and the auto-regression analysis of discrete-time signals are explained along with the concepts of resonance spectra, Fourier spectra, and maximum entropy estimators. We present optimal (Kalman) filtering and independent component analysis. Finally, we outline the methods of state-space reconstruction, a key tool of non-linear time-series analysis based on the Takens embedding theorem. The Examples and Problems range from the computation of auto-correlations in the logistic and standard (Chirikov) maps to phase transitions in the two-dimensional Ising model, the analysis of spectra of acoustic resonators, and the study of electro-cardiograms in the presence of noise.