The Equivalence Principle is an informal principle asserting that equivalent mathematical objects have the same properties.  For example, isomorphic groups should have the same group-theoretic properties, and equivalent categories should have the same category-theoretic properties. Vladimir Voevodsky established Univalent Foundations as a foundation of mathematics (based on dependent type theory) in which this principle cannot be violated -- it is a theorem. In this talk, I will introduce Univalent Foundations (roughly synonymous with homotopy type theory) motivated by this perspective.