Abstract: In this talk we will give a brief introduction to the soliton gas theory based on the focusing nonlinear Schrödinger equation. Following the spectral theory developed by El-Tovbis (PRE2020), we further developed the soliton gas theory and gave mathematical estimates for the continuum limit to the so-called nonlinear dispersion relations (NDR). We then introduce the periodic gas, which brings us an exact solvable model for the first NDR equation. One of the main results in this soliton gas theory is to compute the averaged conserved quantities. In this talk, we will explain how to get those formulae for the fNLS using Forest-Lee’s earlier contributions. In the last part of the talk, we will introduce a different way to formulate soliton gases (condensates) by so-called primitive potential and a recent interesting work called soliton shielding will be mentioned as well.