  We show how several properties of the QCD axion can be extracted at high
precision using only first principle QCD computations. By combining NLO results
obtained in chiral perturbation theory with recent Lattice QCD results the full
axion potential, its mass and the coupling to photons can be reconstructed with
percent precision. Axion couplings to nucleons can also be derived reliably,
with uncertainties smaller than ten percent. The approach presented here allows
the precision to be further improved as uncertainties on the light quark masses
and the effective theory couplings are reduced. We also compute the finite
temperature dependence of the axion potential and its mass up to the crossover
region. For higher temperature we point out the unreliability of the
conventional instanton approach and study its impact on the computation of the
axion relic abundance.
