In the view of transmutation of transuranium (TRU) elements, molten salt fast reactors (MSFRs) offer certain advantages compared to solid fuelled reactor types like sodium cooled fast reactors (SFRs). In the first part these advantages are discussed in comparison with the SFR technology, and the research challenges are analyzed. In the second part cycle studies for the MSFR are given for different configurations--a core with U-238 fertile, a fertile free core, and a core with Th-232 as fertile material. For all cases, the transmutation potential is determined and efficient transmutation performance for the case with thorium as a fertile material as well as for the fertile free case is demonstrated and the individual advantages are discussed. The time evolution of different important isotopes is analyzed. In the third part a strategy for the optimization of the transmutation efficiency is developed. The final aim is dictated by the phase out decision of the German government, which requests to put the focus on the determination of the maximal transmutation efficiency and on an as much as possible reduced leftover of transuranium elements at the end of the reactor life. This minimal leftover is achieved by a two step procedure of a first transmuter operation phase followed by a second deep burning phase. There the U-233, which is bred in the blanket of the core consisting of thorium containing salt, is used as feed. It is demonstrated, that transmutation rates up to more than 90% can be achieved for all transuranium isotopes, while the production of undesired high elements like californium is very limited. Additionally, the adaptations needed for the simulation of a MSFR, and the used tool HELIOS 1.10 is described.