The electronic band structure of the semiconducting \ensuremath{\beta} and \ensuremath{\gamma} polytypes of InSe is calculated from first principles, with spin-orbit effects included. The two polytypes differ by the lateral stacking arrangement of four-atomic-plane building blocks, composed of Se-In-In-Se planes. These building blocks are terminated by Se lone-pair orbitals, which form the electronic states at the valence-band maximum. There is very little bonding between these four-atomic-plane units, and so the band structures of the \ensuremath{\gamma} and \ensuremath{\beta} polytypes are nearly identical, being related simply by zone folding. We find that both materials have direct band gaps (which occur at the \ensuremath{\Gamma} and Z points in the Brillouin zone for the \ensuremath{\beta} and \ensuremath{\gamma} polytypes, respectively), and that there is a large dipole matrix element (i.e., a strong oscillator strength) between the valence maximum and conduction minimum states. These materials are thus potentially significant for light emitting and absorbing devices. In order to study the optical absorption at energies above the band gap, the imaginary part of the dielectric function ${\mathrm{\ensuremath{\epsilon}}}_{2}$(\ensuremath{\omega}) is calculated for \ensuremath{\omega}\ensuremath{\le}12 eV. The effective masses are also calculated: the out-of-plane masses are extremely light, and are equal in magnitude at the valence maximum and conduction minimum states (${\mathit{m}}_{\mathrm{\ensuremath{\perp}}}^{\mathit{c}}$=${\mathit{m}}_{\mathrm{\ensuremath{\perp}}}^{\mathit{v}}$\ensuremath{\approxeq}0.03${\mathit{m}}_{0}$), while the in-plane masses are light for the electrons (${\mathit{m}}_{\mathrm{\ensuremath{\parallel}}}^{\mathit{c}}$\ensuremath{\approxeq}0.1${\mathit{m}}_{0}$) and heavy for the holes (${\mathit{m}}_{\mathrm{\ensuremath{\parallel}}}^{\mathit{v}}$\ensuremath{\approxeq}3${\mathit{m}}_{0}$). The ``anomalous'' mass character (${\mathit{m}}_{\mathrm{\ensuremath{\perp}}}$${\mathit{m}}_{\mathrm{\ensuremath{\parallel}}}$) is explained in terms of intralayer bonding and the lack of lateral bonding between the Se lone-pair orbitals that consitute the valence maximum states.