This text starts with an approach to the theory of multiplicities. It contains as a central topic the Stuckrad-Vogel algorithm and its interpretation in terms o... » 

This text starts with an approach to the theory of multiplicities. It contains as a central topic the Stuckrad-Vogel algorithm and its interpretation in terms of Segre classes. Using the join construction, a proof of Bezout's theorem is given. The theme of Bertini and connectedness is investigated. «