This chapter introduces non-asymptotic methods and concepts in random matrix theory, focusing on the analysis of extreme singular values of random matrices with independent rows or columns. The chapter is divided into several sections, covering preliminaries, random matrices with independent entries, rows, and columns, restricted isometries, and applications in statistics and compressed sensing. Key topics include: 1. **Preliminaries**: Definitions and properties of matrices, singular values, nets, sub-gaussian and sub-exponential random variables, and isotropic random vectors. 2. **Random Matrices with Independent Entries**: Limit laws for Gaussian matrices and general random matrices with independent entries. 3. **Random Matrices with Independent Rows**: Analysis of sub-gaussian and heavy-tailed rows, including applications to estimating covariance matrices and random sub-matrices. 4. **Random Matrices with Independent Columns**: Analysis of sub-gaussian and heavy-tailed columns, including applications to Gram matrices and random Fourier matrices. 5. **Restricted Isometries**: Properties of restricted isometries for sub-gaussian and heavy-tailed random matrices. 6. **Applications**: Applications in statistics (estimating covariance matrices) and compressed sensing (validating measurement matrices). The chapter emphasizes the importance of non-asymptotic methods for understanding the behavior of random matrices in various dimensions, providing tools for practical applications in fields such as statistics, signal processing, and theoretical computer science.This chapter introduces non-asymptotic methods and concepts in random matrix theory, focusing on the analysis of extreme singular values of random matrices with independent rows or columns. The chapter is divided into several sections, covering preliminaries, random matrices with independent entries, rows, and columns, restricted isometries, and applications in statistics and compressed sensing. Key topics include: 1. **Preliminaries**: Definitions and properties of matrices, singular values, nets, sub-gaussian and sub-exponential random variables, and isotropic random vectors. 2. **Random Matrices with Independent Entries**: Limit laws for Gaussian matrices and general random matrices with independent entries. 3. **Random Matrices with Independent Rows**: Analysis of sub-gaussian and heavy-tailed rows, including applications to estimating covariance matrices and random sub-matrices. 4. **Random Matrices with Independent Columns**: Analysis of sub-gaussian and heavy-tailed columns, including applications to Gram matrices and random Fourier matrices. 5. **Restricted Isometries**: Properties of restricted isometries for sub-gaussian and heavy-tailed random matrices. 6. **Applications**: Applications in statistics (estimating covariance matrices) and compressed sensing (validating measurement matrices). The chapter emphasizes the importance of non-asymptotic methods for understanding the behavior of random matrices in various dimensions, providing tools for practical applications in fields such as statistics, signal processing, and theoretical computer science.