Error bounds for the Central Limit Theorem via the Berry–Esseen Theorem and Stein's method

The Central Limit Theorem states that the distribution of the mean of a simple random sample approaches a normal distribution as the sample size increases, regardless of the distribution of the original variables. This theorem is one of the most important in the history of Statistics, as it led to countless mathematical results. The aim of this thesis is to quantify the convergence rate to the normal distribution, providing bounds for the error of approximation of the Central Limit Theorem, using the Berry–Esseen Theorem and Stein's method.