A compact soft X-ray microscope based on a nitrogen double-stream gas puff target soft X-ray source, operating at He-like nitrogen spectral line at the wavelength of λ = 2.88 nm is presented. The desk-top size microscope was successfully demonstrated in transmission mode using the Fresnel zone-plate objective and it is suitable for soft X-ray source microscopy in the "water window" spectral range (λ = 2.3 ÷ 4.4 nm). Details about the soft X-ray source source, the microscope and an example of application in the biomedical field are shown and discussed.