A gas turbine engine booster includes one or more rotatable booster stages having booster blades extending radially inwardly from a rotatable drum and one or more non-rotatable vane stages having booster vanes extending radially outwardly from a non-rotatable shell. The booster stages may be interdigitated with the vane stages. The booster may be co-rotatable or counter-rotatable with respect to a fan stage of an aircraft gas turbine engine. The booster may be driven by a single turbine or one of counter-rotatable turbines or though a gearbox by these turbines. The booster blades and the booster vanes extend across a core engine inlet duct having an entrance downstream of the first fan stage. A fan section with the booster may have counter-rotatable first and second fan stages with fan blades of the second fan stages connected to and mounted radially outwardly of the rotatable drum.