The chapters in this contributed volume explore new results and existing problems in algebra, analysis, and related topics. Chapters are based on talks given at the 2024 "International Conference on Evolution in Pure and Applied Mathematics" (ICEPAM) held at Akal University Talwandi Sabo. Specific topics covered include module theory, non-associative algebras, geometric solitons, graph theory, and more. Algebra, Analysis, and Associated Topics will appeal to researchers, graduate students, and engineers interested in learning more about the impact pure mathematics has on various fields.