This paper introduces a new approach to robust estimation, focusing on the asymptotic theory of estimating a location parameter for contaminated normal distributions. The author, Peter J. Huber, discusses the challenges posed by the contamination of data and proposes a class of estimators called $(M)$-estimators, which are defined by minimizing a function of the errors. These estimators are shown to be asymptotically most robust among all translation-invariant estimators. The paper also explores the asymptotic normality of $(M)$-estimators and provides conditions for their consistency. Additionally, it addresses minimax questions and provides explicit solutions for certain cases. The author concludes by discussing the bias of these estimators and their performance in the presence of asymmetric contaminating distributions. The paper aims to lay the groundwork for a general theory of robust estimation.This paper introduces a new approach to robust estimation, focusing on the asymptotic theory of estimating a location parameter for contaminated normal distributions. The author, Peter J. Huber, discusses the challenges posed by the contamination of data and proposes a class of estimators called $(M)$-estimators, which are defined by minimizing a function of the errors. These estimators are shown to be asymptotically most robust among all translation-invariant estimators. The paper also explores the asymptotic normality of $(M)$-estimators and provides conditions for their consistency. Additionally, it addresses minimax questions and provides explicit solutions for certain cases. The author concludes by discussing the bias of these estimators and their performance in the presence of asymmetric contaminating distributions. The paper aims to lay the groundwork for a general theory of robust estimation.