The Multi-slit Solar Explorer (MUSE) is a proposed mission aimed at understanding the physical mechanisms driving the heating of the solar corona and the eruptions that are at the foundation of space weather. MUSE contains two instruments, a multi-slit EUV spectrograph and a context imager. It will simultaneously obtain EUV spectra (along 37 slits) and context images with the highest resolution in space (0.33-0.4 ) De Pontieu et al. straightforward, as a simultaneous measurement of I(x, y, λ) is always achieved. Detectors for hard X-rays (HXR) provide an energy resolution of a fraction of a keV (Furukawa et al. 2019; Athiray et al. 2017), and a useful resolving power for gamma rays and HXR bremsstrahlung continua, applicable to the very hottest components of the corona, but unfortunately, not for the majority of coronal features that emit EUV. Furthermore, the spatial resolution of state-of-the-art X-ray telescopes (Buitrago-Casas et al. 2017; Chan et al. 2018) is not sufficient to resolve the cross-sectional profiles of bright coronal loops, or their footpoints, where the majority of HXR emission is produced. For soft X-rays (SXR), Bandler et al. (2019) recently demonstrated transition-edge-sensor-based microcalorimeter arrays that provide an energy resolution of 2 eV over the energy range 0.2-7 keV, and thus a resolving power of 3, 500 at 7 keV, but dropping to 100 at ∼ 200eV (∼ 60Å). The count rates for such microcalorimeter systems are limited, and the achievable dynamic range, currently, compromises the utility of such systems for solar observations. Options 2 and 3 can be implemented in a variety of ways, some of which require a sequence of multiple measurements to obtain a single "snapshot" of I(x, y, λ). Analysis of such data is straightforward when the time scales of the process under study are longer than the cycle time of the sequence. Narrow passband filters to implement option 2 are employed at visible, infrared (IR) and radio-frequency (RF) wavelengths, including the measurement of I for multiple polarization states in order to perform spectropolarimetric inversions using visible and near-infrared (NIR) line emission (e.g., Scharmer et al. 2008), and microwave and RF observations of gyroresonance emission, which in combination with high resolution EUV observations can provide valuable diagnostics of the 3D structure of the coronal magnetic field (e.g., Brosius et al. 2002) and electron beams generated in flares and jets (e.g. Chen et al. 2013). Owing ultimately to the low reflectance and transmittance of materials for EUV wavelengths, the achievable resolving power of EUV multilayer coatings for option 2 is only around 10 to 30. A spectrograph, option 3, therefore provides the best resolving power in the EUV.In a traditional imaging spectrograph, light passes through a single entrance slit and is dispersed and re-imaged onto the focal plane. This preserves spatial information in the direction perpendicular