This project focuses on the design, implementation, and validation of a Nonlinear Model Predictive Controller (NMPC) for precise trajectory tracking of a quadrotor system. The goal was to develop a real-time control strategy capable of following complex three-dimensional trajectories while maintaining stability and adhering to the physical limits of the vehicle and its actuators. Quadrotors are inherently nonlinear and underactuated systems, which makes controlling them especially challenging. To address these dynamics, the controller was built around a full-state model derived from the Newton-Euler equations of motion, capturing the system's position, velocity, attitude (expressed in quaternions to avoid singularities), and angular velocity. This detailed modeling allowed the controller to accurately predict the future states of the system and compute optimal control inputs that minimized trajectory error while respecting input and state constraints. The NMPC was formulated and implemented using CasADi for symbolic modeling and acados for real-time optimization, leveraging the High-Performance Interior Point Method (HPIPM) solver and Sequential Quadratic Programming (SQP). The dynamics were discretized using a fourth-order Runge-Kutta integration method, and the cost function was designed to balance position tracking accuracy with control effort by tuning weighting matrices for position, velocity, attitude, and actuator usage. The parameters were iteratively adjusted to refine the trade-off between responsiveness, stability, and computational efficiency. Simulation and validation were carried out in the PyBullet physics engine, providing a realistic environment for evaluating controller performance under various trajectory and disturbance conditions. Several benchmark trajectories were used, including quintic point-to-point motion, circular paths, and lemniscate trajectories. The NMPC achieved high tracking precision with root-mean-square errors below two centimeters on linear trajectories and below ten centimeters on circular paths. Real-time solver performance exceeded 700 Hz, with the optimized SPI-RTI solver reaching computation rates of over 2 kHz, confirming the controller's suitability for embedded real-time flight applications. Disturbance rejection tests demonstrated reasonable robustness under small external forces but also revealed sensitivity to model inaccuracies and infeasible reference trajectories, emphasizing the importance of accurate dynamics modeling and constraint formulation. Overall, the project demonstrated that NMPC offers a powerful and flexible approach to controlling nonlinear aerial systems. The controller achieved smooth, stable, and accurate trajectory tracking while operating well within real-time computational limits. Limitations observed under large disturbances and highly aggressive trajectories provided valuable insights into the need for adaptive or learning-based extensions to improve robustness. Future work will focus on enhancing disturbance rejection, incorporating adaptive gain tuning, and implementing the controller on physical quadrotor hardware for experimental validation. Through this project, I gained extensive experience in nonlinear control theory, dynamic modeling, and real-time optimization. I developed strong proficiency with Python-based control toolchains, including CasADi and acados, and deepened my understanding of numerical methods such as Runge-Kutta integration and quadratic programming. Additionally, I refined my ability to tune control parameters, analyze simulation data, and evaluate system performance using metrics like RMSE and solver frequency. This work reflects a comprehensive integration of theory, computation, and simulation — showcasing my ability to bridge the gap between control design and real-world implementation.