For a human Mars exploration mission, it is required to minimize the time-of-flight of the interplanetary trajectories to mitigate the adverse effects of the radiation environment and prolonged weightlessness conditions on the health of the crew. Moreover, having a fail-safe provision to return the crew back to Earth in case of a mission abort situation is highly desirable. This thesis research investigated several optimal/sub-optimal and feasible solutions for the high-thrust interplanetary transfer and abort trajectories of a reconnaissance human Mars mission. A conjunction-class mission architecture has been analyzed to transport the crew to and from Mars during the transfer opportunities in 2028 and 2030, respectively. Baseline requirements of such a mission were defined by finding the optimal ballistic Earth-to-Mars and Mars-to-Earth transfer trajectory solutions. A number of propulsive abort trajectory solutions were then computed that can return the crew back to Earth when the nominal mission is aborted either during the Earth-to-Mars transfer or during the Mars surface stay period. A semi-analytic trajectory model was used for the design of such abort trajectories that can include one or two deep space maneuvers and a powered Mars swing-by. With the use of a meta-heuristic global optimization algorithm, multi-objective optimization problems were solved to minimize the ΔV cost and the interplanetary transit duration of the mission. By comparing the transfer and abort trajectory solutions, it was concluded that various abort trajectory options can be provided for a reconnaissance human Mars mission, that also satisfy the imposed constraint on the arrival excess velocity. The effects of such abort trajectory options on the ΔV cost and other baseline mission requirements (such as the total mission duration) were analyzed. Critical challenges of such a safe human Mars mission architecture have been identified and discussed.