This lecture covers advanced methods in recommender systems, focusing on matrix factorization to decompose the rating matrix into user and item features. The instructor explains the optimization problem, stochastic gradient descent, regularization, and issues with basic matrix factorization. Various evaluation metrics like RMSE, NDCG, and hit rate are discussed, along with the outlook on Bayesian personalized ranking. The lecture concludes with a summary highlighting the evolution of recommender systems and challenges in scaling to large user populations.