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.
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