Aleksandra Nowel Title: Effective methods for calculating some invariants of real polynomial mappings Abstract: The development of the Gröbner basis theory and Hironaka's results on resolution of singularities benefited to growing importance of effective methods for studying invariants associated with objects of algebraic geometry. The rapid development of computers has enabled the practical use of algorithms which had been worked out. I will present the use of classic results for counting the number of roots of polynomials ("trace formula" - Pedersen, Roy, Szpirglas, Becker, Wörmann) and the local topological degree (Eisenbud, Levine, Khimshiashvili, Szafraniec, Łęcki) using signature of a square form to calculate some invariants of real polynomial mappings.