  The Robertson model describing a chemical reaction involving three reactants
is one of the classical examples of stiffness in ODEs. The stiffness is caused
by the occurrence of three reaction rates $k_1,\,k_2$, and $k_3$, with largely
differing orders of magnitude, acting as parameters. The model has been widely
used as a numerical test problem. Surprisingly, no asymptotic analysis of this
multiscale problem seems to exist. In this paper we provide a full asymptotic
analysis of the Robertson model under the assumption $k_1, k_3 \ll k_2$. We
rewrite the equations as a two-parameter singular perturbation problem in the
rescaled small parameters $(\varepsilon_1,\varepsilon_2):=(k_1/k_2,k_3/k_2)$,
which we then analyze using geometric singular perturbation theory (GSPT). To
deal with the multi-parameter singular structure, we perform blow-ups in
parameter- and variable space. We identify four distinct regimes in a
neighbourhood of the singular limit \mbox{$(\varepsilon_1,\varepsilon_2)=
(0,0)$}. Within these four regimes we use GSPT and additional blow-ups to
analyze the dynamics and the structure of solutions. Our asymptotic results are
in excellent qualitative and quantitative agreement with the numerics.
