  Thanks to their exceptional spatial, spectral and temporal resolution,
highly-coherent free-electron beams have emerged as powerful probes for
material excitations, enabling their characterization even in the quantum
regime. Here, we investigate strong light-matter coupling through monochromatic
and modulated electron wavepackets. In particular, we consider an archetypal
target, comprising a nanophotonic cavity next to a single two-level emitter. We
propose a model Hamiltonian describing the coherent interaction between the
passing electron beam and the hybrid photonic-excitonic target, which is
constructed using macroscopic quantum electrodynamics and fully parameterized
in terms of the electromagnetic Dyadic Green's function. Using this framework,
we first describe electron-energy-loss and cathodoluminescence spectroscopies,
and photon-induced near-field electron emission microscopy. Finally, we show
the power of modulated electrons beams as quantum tools for the manipulation of
polaritonic targets presenting a complex energy landscape of excitations.
