Most of the biopolymers carry ionizable groups and they are Polyelectrolyte. When a Polyelectrolyte is suspended in a polar liquid like water, the tiny oppositely charged particles dissociate from them into the liquid. These tiny particles are counterions and play a crucial role in the behavior of the Polyelectrolytes. One of the most attractive Polyelectrolyte systems is the Polyelectrolyte brush bilayer (PEBB). The PEBB forms when linear Polyelectrolyte chains are grafted densely into two parallel surfaces by one end. The distance between two brush covered surfaces is such that the free ends of the chains interpenetrate into each other. This interpenetration zone also plays a crucial role in defining the major behavior of the system. The PEBBs are found in synovial joints as aggregan and they decrease the friction between the bones in the moving process. The polymer brush bilayers have been studied vastly for decades, however, up to the present there has not been a general and solid theoretical approach to this system. This has been due to the huge complexity of the problem. In this article, I present a solid theoretical approach to the problem of PEBB at thermal equilibrium. This approach is based on the Hirz's master's thesis at Yeshiva University in 1988. In her thesis, Hirz studied polymer brushes by density functional theory (DFT). The DFT is very powerful theoretical tool for studying many body systems and it is used in many research groups around the world.