Explore finite-dimensional DG algebras and categories of perfect complexes in this comprehensive lecture by Dmitri Orlov from the Steklov Mathematical Institute of Russian Academy of Sciences. Delve into the concept of proper derived noncommutative schemes and examine their fundamental properties. Investigate the connection between these categories and DG categories with (semi)exceptional collections. Gain insights into advanced mathematical concepts and their applications in the field of algebraic geometry and noncommutative algebra.