Designed for advanced learners and researchers, the book delivers a rigorous exploration of continuous time formulations that underpin next generation optimization based control strategies. It emphasizes core topics such as gradient flows, Lyapunov stability, finite and fixed time convergence, predefined time stability, and feedback optimization-precisely the themes central to contemporary research in dynamical optimization. The book blends theoretical development with practical insight, supported by worked examples, end of chapter references, and rich visualizations through 80 high quality colour figures. Readers gain a deep understanding of how continuous time models can be leveraged to design robust controllers with guaranteed convergence properties-even in constrained or time varying environments.