In the $Lambda$CDM paradigm the Galactic stellar halo is predicted to harbor the accreted debris of smaller systems. To identify these systems, the H3 Spectroscopic Survey, combined with $Gaia$, is gathering 6D phase-space and chemical information in the distant Galaxy. Here we present a comprehensive inventory of structure within 50 kpc from the Galactic center using a sample of 5684 giants at $|b|>40^{circ}$ and $|Z|>2$ kpc. We identify known structures including the high-$alpha$ disk, the in-situ halo (disk stars heated to eccentric orbits), Sagittarius (Sgr), $Gaia$-Sausage-Enceladus (GSE), the Helmi Streams, Sequoia, and Thamnos. Additionally, we identify the following new structures: (i) Aleph ([Fe/H]$=-0.5$), a low eccentricity structure that rises a surprising 10 kpc off the plane, (ii, iii) Arjuna ([Fe/H]$=-1.2$) and Iitoi ([Fe/H]$<-2$), which comprise the high-energy retrograde halo along with Sequoia, and (iv) Wukong ([Fe/H]$=-1.6$), a prograde phase-space overdensity chemically distinct from GSE. For each structure we provide [Fe/H], [$alpha$/Fe], and orbital parameters. Stars born within the Galaxy are a major component at $|Z|sim$2 kpc ($approx$60$%$), but their relative fraction declines sharply to $lesssim$5$%$ past 15 kpc. Beyond 15 kpc, $>$80$%$ of the halo is built by two massive ($M_{star}sim10^{8}-10^{9}M_{odot}$) accreted dwarfs: GSE ([Fe/H]$=-1.2$) within 25 kpc, and Sgr ([Fe/H]$=-1.0$) beyond 25 kpc. This explains the relatively high overall metallicity of the halo ([Fe/H]$approx-1.2$). We attribute $gtrsim$95$%$ of the sample to one of the listed structures, pointing to a halo built entirely from accreted dwarfs and heating of the disk.
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