Tying Light in Knots

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Focusing on the mathematical foundations of topology, this book explores its crucial role in various fields, including particle physics, solid-state physics, and increasingly in classical and quantum optics. It addresses phenomena such as Pancharatnam-Berry phases and optical vortices, illustrating how topology informs optical applications. The text aims to equip readers with the necessary mathematical tools to understand these concepts and their implications in optical simulations and solid-state topological phenomena.