This thesis explores the domain of machine unlearning, specifically focusing on developing and evaluating different algorithms. These methodologies enable machine learning models to selectively erase the influence of specific data from the training in compliance with privacy regulations such as the GDPR's "Right to be Forgotten." The research introduces a novel unlearning framework designed to optimize unlearning effectiveness without compromising the model’s performance. A significant contribution of this work is the development of a new unlearning method that surpasses existing algorithms in terms of the balance between data forgetting and model utility. This method also allows for a dynamic evaluation of the trade-off between forgetting and retention, ensuring optimal model retraining considering potential constraints.