Lie algebraic deflection aberration theory is presented and applied to combined magnetic focusing-deflection systems. Employing this new algebraic tool, all third- and fifth-order canonical aberrations (including canonical position and momentum aberrations at arbitrary observation planes) for combined systems are derived. The results are complete with concise forms. An example of an in-lens deflection system is calculated for high-order geometric aberrations through fifth order. This article lays the groundwork for further studies on the computation and optimized design for higher-order aberrations of scanning probe systems.