This chapter, authored by J. W. Goodman, delves into the statistical properties of laser speckle patterns, which are significant in various physical phenomena. The author begins by explaining the concept of random walk in the complex plane and derives the first-order statistics of complex amplitude, intensity, and phase of speckle. It also examines the sums of speckle patterns, including partially polarized speckle, and the sum of a speckle pattern and a coherent background. The chapter then explores second-order statistics, such as the autocorrelation function and power spectral density, for both free-space propagation and imaging geometries. Additionally, it discusses the statistics of spatially integrated or blurred speckle patterns and the relationship between surface structure and the resulting speckle pattern, emphasizing the effects of surface autocorrelation and finite roughness. The origin of laser speckle is traced back to the operation of the first continuous-wave (cw) HeNe laser in 1960, which revealed a granular appearance in the images of objects viewed in highly coherent light. This phenomenon, known as "laser speckle," is caused by the interference of many coherent wavelets from different microscopic elements of a rough surface. The chapter explains that speckle can arise from both free-space propagation and imaging operations, where diffraction and interference play crucial roles. The underlying random interference phenomenon in laser speckle has parallels in other branches of physics and engineering, with early mathematical investigations dating back to Verdet.This chapter, authored by J. W. Goodman, delves into the statistical properties of laser speckle patterns, which are significant in various physical phenomena. The author begins by explaining the concept of random walk in the complex plane and derives the first-order statistics of complex amplitude, intensity, and phase of speckle. It also examines the sums of speckle patterns, including partially polarized speckle, and the sum of a speckle pattern and a coherent background. The chapter then explores second-order statistics, such as the autocorrelation function and power spectral density, for both free-space propagation and imaging geometries. Additionally, it discusses the statistics of spatially integrated or blurred speckle patterns and the relationship between surface structure and the resulting speckle pattern, emphasizing the effects of surface autocorrelation and finite roughness. The origin of laser speckle is traced back to the operation of the first continuous-wave (cw) HeNe laser in 1960, which revealed a granular appearance in the images of objects viewed in highly coherent light. This phenomenon, known as "laser speckle," is caused by the interference of many coherent wavelets from different microscopic elements of a rough surface. The chapter explains that speckle can arise from both free-space propagation and imaging operations, where diffraction and interference play crucial roles. The underlying random interference phenomenon in laser speckle has parallels in other branches of physics and engineering, with early mathematical investigations dating back to Verdet.