  A comprehensive set of azimuthal single-spin and double-spin asymmetries in
semi-inclusive leptoproduction of pions, charged kaons, protons, and
antiprotons from transversely polarized protons is presented. These asymmetries
include the previously published HERMES results on Collins and Sivers
asymmetries, the analysis of which has been extended to include protons and
antiprotons and also to an extraction in a three-dimensional kinematic binning
and enlarged phase space. They are complemented by corresponding results for
the remaining four single-spin and four double-spin asymmetries allowed in the
one-photon-exchange approximation of the semi-inclusive deep-inelastic
scattering process for target-polarization orientation perpendicular to the
direction of the incoming lepton beam. Among those results, significant
non-vanishing $\cos{\phi-\phi_S}$ modulations provide evidence for a sizable
worm-gear (II) distribution, $g_{1T}$. Most of the other modulations are found
to be consistent with zero with the notable exception of large $\sin{\phi_S}$
modulations for charged pions and positive kaons.
