The spatial structure of stellar populations with different chemical abundances in the Milky Way (MW) contains a wealth of information on Galactic evolution over cosmic time. We use data on 14,699 red-clump stars from the APOGEE survey, covering 4 kpc∼ R≳15 kpc, to determine the structure of mono-abundance populations (MAPs)-stars in narrow bins in [α/Fe] and [Fe H]-accounting for the complex effects of the APOGEE selection function and the spatially variable dust obscuration. We determine that all MAPs with enhanced [α/Fe] are centrally concentrated and are well-described as exponentials with a scale length of 2.2 ± 0.2 kpc over the whole radial range of the disk. We discover that the surface-density profiles of low-[α/Fe] MAPs are complex: they do not monotonically decrease outwards, but rather display a peak radius ranging from ≈5 to ≈13 kpc at low [Fe H]. The extensive radial coverage of the data allows us to measure radial trends in the thickness of each MAP. While high-[α/Fe] MAPs have constant scale heights, low-[α/Fe] MAPs flare. We confirm, now with highprecision abundances, previous results that each MAP contains only a single vertical scale height and that low- [Fe H], low-[α/Fe] and high-[Fe H], high-[α/Fe] MAPs have intermediate (hZ≈300600 pc) scale heights that smoothly bridge the traditional thin- and thick-disk divide. That the high-[α/Fe], thick disk components do not flare is strong evidence against their thickness being caused by radial migration. The correspondence between the radial structure and chemical-enrichment age of stellar populations is clear confirmation of the inside-out growth of galactic disks. The details of these relations will constrain the variety of physical conditions under which stars form throughout the MW disk.