The algebraic method of renormalization is applied to the standard model of electroweak interactions. We present the most important modifications compared to theories with simple groups. ∗ Presented at the DESY Zeuthen Workshop on Elementary Particle Theory “Loops and Legs in Gauge Theories”, Rheinsberg, Germany, April 19-24, 1998. (1) ALGEBRAIC RENORMALIZATION OF THE ELECTROWEAK STANDARD MODEL