This paper introduces a new approach to studying non-finite symmetries in quantum field theories (QFTs) called Symmetry Theory (SymTh). Unlike Symmetry Topological Field Theories (SymTFTs), which are used to study finite symmetries, SymTh focuses on free theories rather than topological ones. The authors propose a method to extract the symmetry sector of a given QFT by studying the topological operators and boundary conditions in SymTh. They explore this approach through various examples, including abelian \(p\)-form symmetries, 2-groups, and group-like symmetries in quantum mechanics. The paper also derives the SymTh of \(\mathbb{Q}/\mathbb{Z}\) non-invertible symmetries from the dimensional reduction of IIB supergravity on the conifold and discusses how branes can provide a UV interpretation of quantum Hall states dressing non-invertible topological defects. The authors provide a detailed construction of SymTh for a \(U(1)^{(p)}\) symmetry, including the definition of topological operators, boundary conditions, and the sandwich construction, which is analogous to the construction in SymTFTs. They also discuss the relation between their approach and previous work on SymTFTs, particularly in the context of 2D Maxwell and Yang-Mills theories.This paper introduces a new approach to studying non-finite symmetries in quantum field theories (QFTs) called Symmetry Theory (SymTh). Unlike Symmetry Topological Field Theories (SymTFTs), which are used to study finite symmetries, SymTh focuses on free theories rather than topological ones. The authors propose a method to extract the symmetry sector of a given QFT by studying the topological operators and boundary conditions in SymTh. They explore this approach through various examples, including abelian \(p\)-form symmetries, 2-groups, and group-like symmetries in quantum mechanics. The paper also derives the SymTh of \(\mathbb{Q}/\mathbb{Z}\) non-invertible symmetries from the dimensional reduction of IIB supergravity on the conifold and discusses how branes can provide a UV interpretation of quantum Hall states dressing non-invertible topological defects. The authors provide a detailed construction of SymTh for a \(U(1)^{(p)}\) symmetry, including the definition of topological operators, boundary conditions, and the sandwich construction, which is analogous to the construction in SymTFTs. They also discuss the relation between their approach and previous work on SymTFTs, particularly in the context of 2D Maxwell and Yang-Mills theories.