We investigate the analytic, rational and C1 first integrals of the Maxwell–Bloch system
\begin{equation*}
\dot{E}=-\kappa E+gP,\quad \dot{P}=-\gamma _{\bot }P+gE\triangle , \quad \dot{\triangle }=-\gamma _{\Vert }(\triangle -\triangle _0)-4gPE,
\end{equation*}
where κ,γ⊥,g,γ∥,△0 are real parameters. In addition, we prove this system is rationally non-integrable in the sense of Bogoyavlenskij for almost all parameter values