This paper presents Australia Telescope Compact Army H I synthesis observations of the weak blue compact dwarf (BCD) galaxy NGC 2915. It is shown that NGC 2915 has the H I properties of a late-type spiral galaxy (Sd-Sm), including a double horn global profile, and H I spiral arms. The H I extends out to over five times the Holmberg radius, and 22 times the exponential scale length in the B band. The optical counterpart corresponds to a central H I bar. The H I distribution and kinematics are discussed in detail. A rotation curve is derived and fitted with a mass model consisting of a stellar disk, a neutral gas disk, and a dark matter (DM) halo. The DM halo dominates at nearly all radii. The total mass to blue light ratio, M(T)/L(B)=76 within the last measured point. Thus NGC 2915 is one of the darkest disk galaxies known. The complex H I dynamics of the central region results in a high uncertainty of many of the fitted parameters. Nevertheless it is clear that the core of the DM halo is unusually dense (rho(0) approximate to 0.1 M. pc(-3)) and compact (R(c) approximate to 1 kpc). The neutral gas component, with mass M(g)=1.27 X 10(9) M. is probably more massive than the stellar disk. Split and broad H I lines (velocity dispersion approximate to 35 km s(-1)) are seen in the central region. Pressure support is probably significant, and it is not clear whether the core is in equilibrium. Beyond the optical disk the average H I line of sight velocity dispersion is 8 km s(-1), which is normal for disk galaxies. NGC 2915 does not obey the Tully-Fisher [A&A, 54, 661 (1977)] relation, being underluminous for its V-rot=88 km s(-1) by a factor of nine. It also does not obey the star-formation threshold model of Kennicutt [ApJ, 344, 685 (1989)], when only the neutral gas is considered. A simple H I surface density threshold of Sigma(H I,crit)approximate to 10(21) 10(21) cm(-2) adequately describes the location of current star formation. Although the H I properties of NGC 2915 are extreme relative to normal galaxies they appear less extreme in comparison to other BCDs, which have similar radial profiles of H I density and velocity dispersion, and H I extending well beyond the optical disk. (C) 1996 American Astronomical Society.