This text provides an introduction to non-asymptotic analysis of random matrices, focusing on methods and concepts for analyzing extreme singular values of random matrices with independent rows or columns. The author, Roman Vershynin, discusses the application of these methods in theoretical computer science, statistics, and signal processing. The paper covers various types of random matrices, including those with independent entries, rows, and columns, and explores their properties such as restricted isometries. It also discusses the use of nets, sub-gaussian and sub-exponential random variables, and isotropic random vectors in the analysis of random matrices. The paper emphasizes the importance of non-asymptotic results, which provide guarantees up to absolute constants in all dimensions and with high probability. The text includes applications to estimating covariance matrices and validating probabilistic constructions in compressed sensing. It also introduces key concepts such as the spectral norm, covering numbers, and moment generating functions, and discusses their relevance in the analysis of random matrices. The paper concludes with a discussion of related sources and notes on the history and further reading.This text provides an introduction to non-asymptotic analysis of random matrices, focusing on methods and concepts for analyzing extreme singular values of random matrices with independent rows or columns. The author, Roman Vershynin, discusses the application of these methods in theoretical computer science, statistics, and signal processing. The paper covers various types of random matrices, including those with independent entries, rows, and columns, and explores their properties such as restricted isometries. It also discusses the use of nets, sub-gaussian and sub-exponential random variables, and isotropic random vectors in the analysis of random matrices. The paper emphasizes the importance of non-asymptotic results, which provide guarantees up to absolute constants in all dimensions and with high probability. The text includes applications to estimating covariance matrices and validating probabilistic constructions in compressed sensing. It also introduces key concepts such as the spectral norm, covering numbers, and moment generating functions, and discusses their relevance in the analysis of random matrices. The paper concludes with a discussion of related sources and notes on the history and further reading.