In the evolving field of aerial robotics, the precise control and stabilization of Unmanned Aerial Vehicles (UAVs), particularly quadrotors, stand as critical challenges due to their inherent nonlinear dynamics and susceptibility to external disturbances. This study embarks on addressing these challenges by first establishing a comprehensive mathematical model of a quadrotor's dynamics utilizing the Newton-Euler formulation. This foundational model serves as the basis for implementing a Proportional-Integral-Derivative (PID) control strategy, aimed at maintaining the UAV's desired flight trajectory and enhancing its stability against environmental perturbations. The effectiveness of the PID control approach is meticulously evaluated through a series of simulation tests conducted within the MATLAB/Simulink environment, focusing on the quadrotor's pitch, roll, and yaw control channels. The outcomes of these simulations provide convincing evidence of the PID scheme's ability to ensure rapid response times and precise attitude regulation, underpinning its viability for robust quadrotor UAV operations across diverse operational scenarios. Moreover, this research not only establishes a critical step towards the autonomous operation of UAVs but also accentuates the significance of sophisticated control mechanisms in the advancement of aerial robotics technology.