Tying Light in Knots

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Focusing on the mathematical foundations of topology, this book explores its critical role in both classical and quantum optics, alongside its longstanding applications in particle and solid state physics. It addresses key phenomena such as Pancharatnam-Berry phases, optical vortices, and solitons, highlighting their topological aspects. The text offers a concise overview of the necessary mathematical concepts and a survey of optical applications where these topological principles are significant, making it an essential resource for understanding these advancements.