New extreme ultraviolet (EUV) spectroscopic diagnostics of relatively low-temperature plasmas based on the application of an EUV spectrometer and fast EUV diodes combined with glass capillary optics is described. An advanced high resolution dispersive element sliced multilayer grating was used in the compact EUV spectrometer. For monitoring of the time history of radiation, filtered fast EUV diodes were used in the same spectral region (>13 nm) as the EUV spectrometer. The radiation from the plasma was captured by using a single inexpensive glass capillary that was transported onto the spectrometer entrance slit and EUV diode. The use of glass capillary optics allowed placement of the spectrometer and diodes behind the thick radiation shield outside the direction of a possible hard x-ray radiation beam and debris from the plasma source. The results of the testing and application of this diagnostic for a compact laser plasma source are presented. Examples of modeling with parameters of plasmas are discussed.