This Element provides an entry point for philosophical engagement with quantization and the classical limit. It introduces the mathematical tools of C*-algebras as they are used to compare classical and quantum physics. It then employs those tools to investigate philosophical issues surrounding theory change in physics. It discusses examples in which quantization bears on the topics of reduction, structural continuity, analogical reasoning, and theory construction. In doing so, it demonstrates that the precise mathematical tools of algebraic quantum theory can aid philosophers of science and philosophers of physics.

This Element offers an overview of some of the most important debates in philosophy and physics around the topics of emergence and reduction and proposes a compatibilist view of emergence and reduction. In particular, it suggests that specific notions of emergence, which the author calls 'few-many emergence' and 'coarse-grained emergence', are compatible with 'intertheoretic reduction'. Some further issues that will be addressed concern the comparison between parts-whole emergence and few-many emergence, the emergence of effective (-field) theories, the use of infinite limits, the notion of intertheoretic reduction and the explanation of universal and cooperative behavior. Although the focus will be principally on classical phase transitions and other examples from condensed matter physics, the main aim is to draw some general conclusions on the topics of emergence and reduction that can help us understand a variety of case-studies ranging from high-energy physics to astrophysics.