In this talk, we consider a least squares nonconforming finite element of low order for solving the transport equations. We give a detailed overview on the stability and the convergence properties of our considered methods in the stability norm. Moreover, we derive residual type a posteriori error estimates for the least squares nonconforming finite element methods under H1 -norm, which can be used as the error indicators to guide the mesh refinement procedure in the adaptive finite element method. The theoretical results are supported by a series of numerical experiments.