Highly accurate mass measurements of exotic nuclides are relevant for the investigation of the structure of the nucleus, the development of mass models and to understand and model astrophysical nucleosynthesis processes. Production, preparation and measurement methods for exotic nuclides are limited by isobaric contamination, required measurement time and number of produced particles. A new alternative to existing methods to circumvent these limitations exists: Multiple-reflection time-of-flight mass spectrometry (MR-TOF-MS). In this thesis, a novel device for isobar separation and direct mass measurement at an ISOL facility will be presented as well as first direct mass measurements of an MR-TOF-MS at an in-flight facility.The TITAN MR-TOF-MS will produce isobarically clean beams, used as a complementary method for mass measurement of very short-lived nuclides and for optimization of the setup. The concept of the device will be presented as well as its design, commissioning and first results achieved in Germany and in Canada. A mass resolving power of 47,000 and a separation power of 14,000 have been reached.By doubling the kinetic energy to its design value and further optimization, a mass resolving power of 100,000 and a separation power of 50,000 will be reached. After its integration into the TITAN setup, the MR-TOF-MS will play an important role in experiments with exotic nuclides in the TITAN setup. Measurements of neutron rich cadmium isotopes are planned.Furthermore, the FRS Ion Catcher is described. As a pilot experiment for the low-energy branch of the Super-FRS of the future facility FAIR, the direct mass measurement of short-lived, heavy nuclides is presented. In the scope of this thesis, the masses of Fr-213 and Rn-213 were measured. This is the first direct mass measurement of Rn-213, a nuclide with a half-life of 19.5 ms. An accuracy of 10^-6 with just 27 measured particles has been achieved.With the developed data evaluation method and improvements in the electronics and settings of the system, accuracies of 3 x 10^-7 are in reach. Measurements on exotic nuclides are planned, findings from the performed measurement will be used to finalize the design of the instruments of the LEB.
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