This chapter introduces the fundamental concepts and methods of optimal control theory applied to biological models. It begins by motivating the problem with a classic example from plant growth dynamics, where the goal is to optimize the allocation of resources between vegetative and reproductive growth. The chapter then delves into the mathematical framework of optimal control, defining key terms and concepts such as piecewise continuous functions, piecewise differentiable functions, and convexity. It presents the necessary conditions for optimality, derived using Pontryagin's Maximum Principle, which involves the Hamiltonian and adjoint equations. The chapter includes examples and exercises to illustrate the application of these concepts, providing a practical understanding of how to solve optimal control problems in biological contexts. The examples cover minimization and maximization problems, and the exercises encourage readers to apply the theory to specific scenarios.This chapter introduces the fundamental concepts and methods of optimal control theory applied to biological models. It begins by motivating the problem with a classic example from plant growth dynamics, where the goal is to optimize the allocation of resources between vegetative and reproductive growth. The chapter then delves into the mathematical framework of optimal control, defining key terms and concepts such as piecewise continuous functions, piecewise differentiable functions, and convexity. It presents the necessary conditions for optimality, derived using Pontryagin's Maximum Principle, which involves the Hamiltonian and adjoint equations. The chapter includes examples and exercises to illustrate the application of these concepts, providing a practical understanding of how to solve optimal control problems in biological contexts. The examples cover minimization and maximization problems, and the exercises encourage readers to apply the theory to specific scenarios.