  We present a strong lensing mass model of Abell 1689 which resolves
substructures ~25 kpc across (including about ten individual galaxy subhalos)
within the central ~400 kpc diameter. We achieve this resolution by perfectly
reproducing the observed (strongly lensed) input positions of 168 multiple
images of 55 knots residing within 135 images of 42 galaxies. Our model makes
no assumptions about light tracing mass, yet we reproduce the brightest visible
structures with some slight deviations. A1689 remains one of the strongest
known lenses on the sky, with an Einstein radius of RE = 47.0" +/- 1.2" (143
+3/-4 kpc) for a lensed source at zs = 2. We find a single NFW or Sersic prole
yields a good fit simultaneously (with only slight tension) to both our strong
lensing (SL) mass model and published weak lensing (WL) measurements at larger
radius (out to the virial radius). According to this NFW fit, A1689 has a mass
of Mvir = 2.0 +0.5/-0.3 x 10^15 Msun / h70 (M200 = 1.8 +0.4/-0.3 x 10^15 Msun /
h70) within the virial radius rvir = 3.0 +/- 0.2 Mpc / h70 (r200 = 2.4
+0.1/-0.2 Mpc / h70), and a central concentration cvir = 11.5 +1.5/-1.4 (c200 =
9.2 +/- 1.2). Our SL model prefers slightly higher concentrations than previous
SL models, bringing our SL+WL constraints in line with other recent
derivations. Our results support those of previous studies which find A1689 has
either an anomalously large concentration or significant extra mass along the
line of sight (perhaps in part due to triaxiality). If clusters are generally
found to have higher concentrations than realized in simulations, this could
indicate they formed earlier, perhaps as a result of early dark energy.
