This chapter explores convolution, cross-correlation, and stochastic analysis for signal processing and random signal analysis. It begins by examining convolution in both continuous and discrete forms, highlighting applications such as determining inverse Laplace transforms, Volterra integral solutions, signal filtering, time series analysis, and image processing. The section on circular convolution addresses techniques for efficiently processing periodic data. The chapter then introduces probability theory, covering its historical roots, fundamental principles, joint probability distributions, and applications in random signal analysis. It discusses the role of convolution in probability distributions, especially in relation to the central limit theorem and other statistical properties. Cross-correlation is introduced as a method to measure similarities between signals or datasets, with detailed coverage of its mathematical properties and applications in stochastic system analysis. This chapter integrates these tools, making it a valuable resource for theoretical and practical applications across diverse fields.