Complex sentence: In 1971 von Beust became member of the conservative Christian Democratic Union (CDU) and in 1973 after finishing highschool he became debuty of the CDU fraction of Hamburg's city-state (parliament) called "Bürgerschaft" until he started to study law in 1975.
Split into simpler sentences: In 1971 von Beust became member of the conservative Christian Democratic Union (CDU). In 1973, after finishing high school, he became deputy of the CDU fraction of Hamburg's city-state parliament ("Bürgerschaft"), a position he held until he started to study law in 1975.