Welcome to the mathematical engine room of modern economics. This primer is designed to demystify the core mathematical tools that economists use to model and understand the forces behind long-term economic growth. To grasp how economists formalize concepts like progress, savings, and consumption over decades, one must first understand the language they use—the language of dynamic optimization. We will explore this essential tool and then see it in action through two foundational paradigms of growth theory: the Cass-Koopmans-Ramsey model, which represents the pinnacle of neoclassical thought, and the AK model, which launched the modern theory of endogenous growth.