With increasing miniaturization in industry and medical technology, non-destructive testing techniques are an area of ever-increasing importance. In this framework, X-ray microscopy offers an efficient tool for the analysis, understanding, and quality assurance of microscopic samples, in particular as it allows reconstructing three-dimensional data sets of the whole sample's volume via computed tomography (CT). The following article describes a compact X-ray microscope in the hard X-ray regime around 9 keV, based on a highly brilliant liquid-metal-jet source. In comparison to commercially available instruments, it is a hybrid that works in two different modes. The first one is a micro-CT mode without optics, which uses a high-resolution detector to allow scans of samples in the millimeter range with a resolution of 1 μm. The second mode is a microscope, which contains an X-ray optical element to magnify the sample and allows resolving 150 nm features. Changing between the modes is possible without moving the sample. Thus, the instrument represents an important step towards establishing high-resolution laboratory-based multi-mode X-ray microscopy as a standard investigation method.