We　present　a　comprehensive　theory　for　interrogation　of　the　quantum　state　of　a　two-level　system　(TLS)　based　on　a　free-electron-bound-electron　resonant　interaction　scheme.　The　scheme　is　based　on　free　electrons,　whose　quantum　electron　wavefunction　is　preshaped　or　optically　modulated　by　lasers　in　an　electron　microscope　setup　and　then　inelastically　scattered　by　a　quantum　TLS　target　(e.g.,　atom,　quantum　dot,　and　crystal　defect　center)　upon　traversing　in　proximity　to　the　target.　Measurement　of　the　postinteraction　energy　spectrum　of　the　electrons　probes　and　quantifies　the　full　Bloch　sphere　parameters　of　a　pre-excited　TLS　and　enables　coherent　control　of　the　qubit　states.　The　exceptional　advantage　of　this　scheme　over　laser-based　ones　is　atomic-scale　spatial　resolution　of　addressing　individual　TLS　targets.　Thus,　this　scheme　opens　horizons　for　electron　microscopy　in　material　interrogation　and　quantum　information　technology.　©　2022　authors.　Published　by　the　American　Physical　Society.