Transition-edge sensors (TESs) are highly-sensitive detectors capable of both radiative flux and single photon measurements. TESs have found a number of applications including astronomical photon measurements, neutrino mass measurements and in the search for dark matter. Despite this versatility, the use of TESs as massive particle spectrometers has received remarkably little attention, notably within the field of electron spectroscopy where TESs could provide significant advantages over existing electron spectrometers. In this thesis, I present the first investigation into the capabilities of TESs in electron spectroscopy using a combination of numerical simulations and experimental measurements. Through the use of numerical simulations, I show that TESs are capable of matching the energy resolution of traditional electron spectrometers whilst providing order of magnitude improvements in measurement efficiency. I then describe the design and testing of a TES electron detection system that I used to perform a set of proof-of-principle TES electron measurement experiments. The results of these experiments are presented, showing the successful detection and energy measurement of individual electrons with energies spanning between 0 and 2000 eV with an energy resolution of 3 eV. An important consideration for TES electron spectrometers is their sensitivity to electric and magnetic fields arising from nearby electron optical components. The sensitivity of TESs to magnetic fields has been investigated before, but the impact of strong electrostatic fields on TESs has not been. I show that the application of electric fields up to 90 kV m⁻¹ had no observable effect on the TESs tested, demonstrating that TESs can be operated in strong DC field environments, as may be found in TES electron spectrometers. Having demonstrated the suitability of TESs as electron spectrometers, I then present designs for a set of TESs, made specifically for electron calorimetry with a dedicated electron absorber structure. I show the results of a set of electron absorption measurements used to determine appropriate materials to be used in this structure. I conclude the thesis by summarising the capabilities and benefits of TES electron spectroscopy as well as the challenges that will need to be overcome to realise this technology.