This book features a thoughtfully curated collection of research contributions spanning regularization theory, integral equations, learning theory, and matrix and operator theory. These contributions were presented in honor of Prof. M. Thamban Nair on his 65th birthday during the International Conference on Analysis, Inverse Problems, and Applications, which took place at the IIT Madras in Chennai, India, from July 18-21, 2022. The book is a valuable resource for graduate students, engineers, scientists, and researchers looking to advance their work in the development of innovative regularization algorithms. It comprises 14 chapters contributed by esteemed experts and emerging researchers.