Adelic spaces are mathematical structures that arise in number theory, particularly in the study of algebraic varieties and arithmetic geometry. They combine local and global properties of numbers by using the concept of adeles, which are elements that capture information from both local fields (like the p-adic numbers) and the global field (like the rational numbers). In essence, adelic spaces allow mathematicians to analyze objects in a unified way, considering all possible places (local and global) simultaneously. This framework is useful for understanding the behavior of solutions to equations over different number systems and plays a crucial role in modern number theory and arithmetic geometry.