  We study all the possible spin asymmetries that can arise in back-to-back
electron-jet production, $ep\rightarrow e+\text{jet}+X$, as well as the
associated jet fragmentation process, $ep\rightarrow e+ \text{jet} (h)+X$, in
electron-proton collisions. We derive the factorization formalism for these
spin asymmetries and perform the corresponding phenomenology for the kinematics
relevant to the future electron ion collider. In the case of unpolarized
electron-proton scattering, we also give predictions for azimuthal asymmetries
for the HERA experiment. This demonstrates that electron-jet production is an
outstanding process for probing unpolarized and polarized transverse momentum
dependent parton distribution functions and fragmentation functions.
