The book will contain refereed articles by the invited speakers on the 2024 AMP conference to be held during August 5-17, 2024 online. AMP stands for Analysis and Mathematical Physics. It brings leading experts in their fields, delivering 1-hour lectures in their field of expertise. There are 28 invited speakers, and there will also be many participants attending the online conference without presenting talks. The conference will concentrate on the following topics: Inverse problems for nonlocal operators Orthogonal polynomials, Jacobi and CMV matrices Quantum graphs Applications of spectral and scattering theory to quantum mechanics and plasma physics Differential operators on closed sets Differential operators on spatial networks Direct and inverse spectral and scattering theory for differential and difference equations and for systems of such equations The aim of the conference is to bring together leading experts and young researchers from all over the world who work in the area of mathematical physics. It promotes exchange of ideas and develops future scientific collaborations and strengthens existing collaborations. The online conference will be broadcast live on a zoom webinar broadcast on Facebook and Youtube channels of IIMAS of UNAM. The list of the speakers and the details for the conference can be found at the conference webpage: https://www.iimas.unam.mx/amp2024/