The subject of these short lecture notes is a recently emerging area within proof theory, called \emph{Universal Proof Theory}. Here one is concerned with the existence and nonexistence of good (or useful or applicable or ...) proof systems.

翻译：这些简短讲义的主题是证明论中一个新兴的领域，称为“通用证明论”。该领域关注的是好的（或有用的、可应用的等）证明系统的存在性与不存在性问题。