The NASA Solar Dynamics Observatory (SDO), scheduled for launch in 2008, incorporates a suite of instruments including the EUV Variability Experiment (EVE). The EVE instrument package contains grating spectrographs used to measure the solar extreme ultraviolet (EUV) irradiance from 0.1 to 105 nm. The Multiple EUV Grating Spectrograph (MEGS) channels use concave reflection gratings to image solar spectra onto CCDs that are operated at -100°C. MEGS provides 0.1nm spectral resolution between 5-105nm every 10 seconds with an absolute accuracy of better than 25% over the SDO 5-year mission. MEGS-A utilizes a unique grazing-incidence, off-Rowland circle (RC) design to minimize angle of incidence at the detector while meeting high resolution requirements. MEGS-B utilizes a double-pass, cross-dispersed double-Rowland circle design. MEGS-P, a Ly-α monitor, will provide a proxy model calibration in the 60-105 nm range. Finally, the Solar Aspect Monitor (SAM) channel will provide continual pointing information for EVE as well as low-resolution X-ray images of the sun. In-flight calibrations for MEGS will be provided by the on-board EUV Spectrophotometer (ESP) in the 0.1-7nm and 17-37nm ranges, as well as from annual under-flight rocket experiments. We present the methodology used to develop the MEGS optical design.