Was Tywin Lannister a villain?

I think that Tywin was one of the biggest villains in Game of Thrones. Though a very intelligent and formidable man, he only cared himself and his family legacy, and didn't really give a damn about the feelings of his actual family members. He married off Cersei to Robert Baratheon against her will and then tried to pair her up with Loras Tyrell, as well as hating Tyrion all of his life and treating him appallingly. He also committed numerous war crimes, including ordering murder of the Targaryens and Martells, and having his troops massacre the prisoners at Harrenhal, as well as orchestrating the Red Wedding. A really nasty piece of work and definitely a baddie.