The chapter introduces the adaptive lasso, a method for simultaneous estimation and variable selection in linear regression models. It begins by discussing the fundamental goals of statistical learning: ensuring high prediction accuracy and identifying relevant predictive variables. The chapter highlights the limitations of traditional methods like ordinary least squares (OLS) and stepwise selection, which often suffer from computational infeasibility and high variability. The lasso (Tibshirani, 1996) is introduced as a regularization technique that addresses these issues by incorporating an $\ell_1$ penalty, which shrinks coefficients towards zero. However, the chapter notes that while the lasso is effective, it may not always achieve the oracle properties—i.e., it may not consistently select the true subset of predictors and may produce biased estimates for large coefficients. To address these limitations, the adaptive lasso is proposed. This method uses adaptive weights, which are data-dependent and chosen to improve the selection accuracy. The chapter proves that under certain conditions, the adaptive lasso enjoys oracle properties, including consistency in variable selection and asymptotic normality. The adaptive lasso is shown to be computationally efficient, as it can be solved using the same algorithms as the lasso. The chapter also discusses the extension of the adaptive lasso to generalized linear models (GLMs) and high-dimensional data. It provides theoretical results and simulation studies to demonstrate the effectiveness of the adaptive lasso in various scenarios. The results support the use of the $\ell_1$ penalty in statistical modeling, highlighting its competitive performance compared to other methods. Finally, the chapter concludes by emphasizing the importance of the adaptive lasso in practical applications, noting that while it may not always dominate other methods in terms of prediction accuracy, it consistently selects the true subset of predictors and provides unbiased estimates for large coefficients.The chapter introduces the adaptive lasso, a method for simultaneous estimation and variable selection in linear regression models. It begins by discussing the fundamental goals of statistical learning: ensuring high prediction accuracy and identifying relevant predictive variables. The chapter highlights the limitations of traditional methods like ordinary least squares (OLS) and stepwise selection, which often suffer from computational infeasibility and high variability. The lasso (Tibshirani, 1996) is introduced as a regularization technique that addresses these issues by incorporating an $\ell_1$ penalty, which shrinks coefficients towards zero. However, the chapter notes that while the lasso is effective, it may not always achieve the oracle properties—i.e., it may not consistently select the true subset of predictors and may produce biased estimates for large coefficients. To address these limitations, the adaptive lasso is proposed. This method uses adaptive weights, which are data-dependent and chosen to improve the selection accuracy. The chapter proves that under certain conditions, the adaptive lasso enjoys oracle properties, including consistency in variable selection and asymptotic normality. The adaptive lasso is shown to be computationally efficient, as it can be solved using the same algorithms as the lasso. The chapter also discusses the extension of the adaptive lasso to generalized linear models (GLMs) and high-dimensional data. It provides theoretical results and simulation studies to demonstrate the effectiveness of the adaptive lasso in various scenarios. The results support the use of the $\ell_1$ penalty in statistical modeling, highlighting its competitive performance compared to other methods. Finally, the chapter concludes by emphasizing the importance of the adaptive lasso in practical applications, noting that while it may not always dominate other methods in terms of prediction accuracy, it consistently selects the true subset of predictors and provides unbiased estimates for large coefficients.