We develop a series of new analytical expressions describing the physical properties of the kinetic Alfv¿n wave. The wave becomes strongly compressive when k⊥-1 is of the order of the ion inertial length. Thus, in a low-&bgr; plasma, the kinetic Alfv¿n wave can be compressive at values of k⊥ for which the dispersion relation departs only slightly from that of the usual MHD Alfv¿n wave. The compression is accompanied by a magnetic field fluctuation ΔB∥ such that the total pressure perturbation Δptot≈0. Thus the wave undergoes transit-time damping as well as Landau damping; the two effects are comparable if the ion thermal speed is of the order of the Alfv¿n speed. We find that the transverse electric field is elliptically polarized but rotating in the electron sense; this surprising behavior of the polarization of the Alfv¿n branch was discovered numerically by Gary [1986>. We derive a new dispersion relation which explicitly shows how the kinetic Alfv¿n wave takes on some properties of the large-k⊥ limit of the slow mode. We also derive approximate dispersion relations valid for a multi-ion plasma with differential streaming. We suggest that the kinetic Alfv¿n wave may be responsible for the flattening of density fluctuation spectra observed at large wavenumbers in the corona and in the solar wind. We also find that our derived properties of the kinetic Alfv¿n wave are consistent with its presence in the dissipation range of MHD turbulence [Leamon et al., 1998a, b>. ¿ 1999 American Geophysical Union