  Combining with the small-large black hole phase transition, the thermodynamic
geometry has been well applied to study the microstructure for the charged AdS
black hole. In this paper, we extend the geometric approach to the rotating
Kerr-AdS black hole and aim to develop a general approach for the Kerr-AdS
black hole. Treating the entropy and pressure as the fluctuation coordinates,
we construct the Ruppeiner geometry for the Kerr-AdS black hole by making the
use of the Christodoulou-Ruffini-like squared-mass formula, which is quite
different from the charged case. Employing the empirical observation of the
corresponding scalar curvature, we find that, for the near-extremal Kerr-AdS
black hole, the repulsive interaction dominates among its microstructure. While
for far-from-extremal Kerr-AdS black hole, the attractive interaction
dominates. The critical phenomenon is also observed for the scalar curvature.
These results uncover the characteristic microstructure of the Kerr-AdS black
hole. Such general thermodynamic geometry approach is worth generalizing to
other rotating AdS black holes, and more interesting microstructure is expected
to be discovered.
