The development and demonstration of a soft X-ray (SXR) microscope, based on a Z-pinching capillary discharge source has been realized. The Z-pinching plasma acts as a source of SXR radiation. A ceramic capacitor bank is pulsed charged up to 80 kV, and discharged through a pre- ionized nitrogen filled ceramic capillary. The discharge current has an amplitude of ~25 kA. Working within the water-window spectral region (λ = 2.88 nm), corresponding to the 1s2-1s2p quantum transition of helium-like nitrogen (N5+), the microscope has a potential in exploiting the natural contrast existing between the K-absorption edges of carbon and oxygen as the main constituents of biological materials, and hence imaging them with high spatial resolution. The SXR microscope uses the grazing incidence ellipsoidal condenser mirror for the illumination, and the Fresnel zone plate optics for the imaging of samples onto a BI-CCD camera. The half- pitch spatial resolution of 100 nm  was achieved, as demonstrated by the knife-edge test. In order to enhance the photon-flux at the sample plane, a new scheme for focusing the radiation, from multiple capillary sources has been investigated. Details about the source, and the construction of the microscope are presented and discussed.