In this talk, I will first introduce the physical and biomedical background of the quantitative photoacoustic tomography (qPAT). The quantitative step has been traditionally using the diffusion approximation to solve but fails at many scenarios in practice. In recent years, more and more researches start to use the transport model to study this problem. However there are still some open problems relating to the uniqueness and stability estimates. We will try to study the qPAT with the simplified PN approximation which is regarded as a more accurate approximation than the simplest diffusion approximation. I will show that the uniqueness and stability estimates under this formulation. Numerical experiments are performed to validate the theory.