QCD thermodynamics within Hard Thermal loop perturbation theory and beyond

Hard Thermal Loop perturbation theory (HTLpt) is one of the most successful theory to study the bulk thermodynamical quantities of hot and dense deconfined nuclear matter. In HTLpt, the constituent quark masses are being neglected and electric scale is being resummed. To extend the applicability of the HTLpt, magnetic scale resummation in HTLpt is also proposed in recent years. Along with the magnetic scale resummation, recently we have reformulated HTLpt with finite quark masses. In addition to those, we have also reformulated HTLpt for magnetized hot and dense nuclear matter and applied that results to calculate QCD thermodynamics in one-loop level. In this talk, I shall show the existing three-loop QCD thermodynamic results that has been obtained using normal HTL. I shall also show the available thermodynamic result with magnetic scale resummation and also with finite quark masses. I shall also discuss the reformulation of HTLpt for magnetized medium and the QCD pressure for such medium.