Complex sentence: In the following years under Charles of Lorraine Imperial Habsburg armies conquered many fortresses (such as Esztergom, Vác, Pest), which were under Ottoman rule, and after the Battle of Buda they laid siege to and took over the former Hungarian capital of Buda.
Split into simpler sentences: In the following years, the Imperial Habsburg armies under Charles of Lorraine drove the Osmans back, conquering from them many fortresses (such as Esztergom, Vác, Pest). After the Battle of Buda they laid siege to and took over the former Hungarian capital of Buda.