The thesis is dealing with a special type of recommender system, with the main focus on the item and model based collaborative filtering recommender system including corresponding SVD based algorithm. The historical overview of recommender systems is briefly illustrated, key terms are listed and the most important types of recommender systems are described. Afterwards, the central algorithm of the thesis, the SVD algorithm for recommender system with dimensionality reduction, has been stated and its utility is motivated. The benefit of SVD decomposition in the real world has been outlined while describing properties of the central algorithm. After that, the folding-in method and the update method for updating system with new users have been described and related algorithms are given. The last section of the thesis displays the test examples of implemented algorithms, the central algorithm of the thesis and the folding-in method. Code implementation using Matlab is appended at the end of the thesis in Appendix 2 and Appendix 3.