In recent years, the world has witnessed significant progress in optimization for emerging fields, including meta-learning, fine-tuning, automated hyperparameter selection, continual learning, fair batch selection, adversarial learning, and artificial intelligence (AI)-aware communication networks. Problems arising from these fields often exhibit a common nested optimization structure, which has motivated the study of bilevel optimization. However, there are many theoretical and computational challenges in large-scale bilevel optimization problems, e.g., those arising from machine learning on massive amounts of data in high-dimensional feature domains that have manifold constraints. This project will provide a comprehensive study of bilevel optimization theory, algorithms, and applications for large-scale problems. The outcomes of this project will benefit researchers in academia, government labs, and industry aiming to solve large-scale nested optimization problems in science and engineering. New applications in information science, signal processing, communications, statistics, and machine learning will be studied. This project consists of three intertwined thrusts. The first thrust focuses on developing fast and scalable Hessian-free bilevel algorithms with convergence rate guarantees. Specifically, several Hessian-free approaches will be designed and analyzed using methods of fully single-loop momentum, finite-difference matrix-vector estimation, and residual response