The purpose if this master's thesis is to study and develop a new algorithmic framework for Collaborative Filtering to produce recommendations in the top-N recommendation problem. Thus, we propose Lanczos Latent Factor Recommender (LLFR); a novel "big data friendly" collaborative filtering algorithm for top-N recommendation. Using a computationally efficient Lanczos-based procedure, LLFR builds a low dimensional item similarity model, that can be readily exploited to produce personalized ranking vectors over the item space. A number of experiments on real datasets indicate that LLFR outperforms other state-of-the-art top-N recommendation methods from a computational as well as a qualitative perspective. Our experimental results also show that its relative performance gains, compared to competing methods, increase as the data get sparser, as in the Cold Start Problem. More specifically, this is true both when the sparsity is generalized - as in the New Community Problem, a very common problem faced by real recommender systems in their beginning stages, when there is not sufficient number of ratings for the collaborative filtering algorithms to uncover similarities between items or users - and in the very interesting case where the sparsity is localized in a small fraction of the dataset - as in the New Users Problem, where new users are introduced to the system, they have not rated many items and thus, the CF algorithm can not make reliable personalized recommendations yet.