Aspects of (generalized) symmetries

In this thesis, we present various aspects of generalized symmetries in quantum field theory and holography. After a brief introduction to the subject, we analyze various examples in which the symmetry structure is quite peculiar and extends beyond the standard framework of global symmetries as group-like transformations of local op erators. The modern approach to this subject relies on the correspondence between symmetries and topological operators within a given quantum theory. In the first part of this dissertation, we analyze theories in which the set of topological operators can extend beyond groups (also known as non-invertible symmetries) and explore sit uations in which a symmetry broken by a deformation can re-emerge after ensemble averaging. In the second part of the thesis, we examine how special non-invertible symmetries arise in the holographic duals of certain supersymmetric quantum field theories. This holographic understanding proves to be useful in comprehending the intricate structure of these particular symmetries, revealing properties that might be challenging to grasp solely from a quantum field theory perspective.