This study presents a quaternion formulation of classical electrodynamics in the absence of magnetic monopoles. The primary objective is to reformulate Maxwell's theory using quaternion algebra while preserving the physical predictions of classical electrodynamics. The analysis focuses on expressing electromagnetic quantities, including the four-current, four-potential, differential operator, and field equations, within a unified quaternion framework.The principal contribution of this work is the reformulation of Maxwell's equations in quaternion form. Rather than employing multiple independent vector equations, the quaternion formalism consolidates them into a compact set of equations without altering the physical content of Maxwell's theory. This approach simplifies the mathematical structure while maintaining equivalence with the classical formulation. The electric field, magnetic field, and propagation vector remain mutually perpendicular, demonstrating that the quaternion approach is consistent with classical electromagnetic wave theory. Additionally, the quaternion equations reduce the number of separate mathematical expressions while preserving Lorentz covariance. This compact formulation is both mathematically elegant and well-suited electrodynamics.