Fundamental understanding and engineering of composite materials, biological structures and buildingblocks for electrical and optical devices of nanoscale dimensions necessitate the availability of advancedmicroscopy tools for mapping their local chemical, structural and free-carrier properties. But while opticalspectroscopy, particularly in the infrared (IR) and terahertz (THz) frequency range, has tremendous merit inmeasuring such properties optically, the diffraction-limited spatial resolution has been preventing IR andTHz microscopy applications for the longest time to be used in nanoscale materials and device analysis, bioimaging,industrial failure analysis and quality control.During the last years we pioneered the field of IR and THz near-field microscopy, which allows twodimensional(2D) spectroscopic IR and THz imaging of a sample surface with nanoscale spatial resolution,independent of the wavelength. Key achievements of our work are the nanoscale resolved near-field mappingof chemical compositions of polymer blends, mechanical strain fields in ceramics and free-carrierconcentrations in doped semiconductor transistors.The core objective of this proposal is to develop a three-dimensional (3D) spectroscopic imaging method ina wide spectral range between infrared (IR) and terahertz (THz) frequencies with nanoscale spatialresolution, a method that does not and not even nearly exist today. Our approach will be based on scatteringtypescanning near-field optical microscopy (s-SNOM), even though s-SNOM is generally considered to be asurface mapping technique. Instead of scanning the surface, it is proposed to scan a volume above the samplesurface. By using appropriate reconstruction methods, the three-dimensional structure of the sample volumebelow the sample surface could be obtained in principle. We recently conducted a theoretical study, whichconfirmed the fundamental feasibility of this novel approach that shall be experimentally realized within thisproposal.The proposed method of IR and THz nanotomography could become a new paradigm in nanoscale opticalimaging. Near-field nanotomography will have the potential to open new and even unexpected avenues foroptical characterization throughout all nanosciences, such as non-invasive, chemical identification of single(biological) nanoparticles in complex 3D-nanostructures or the measurement of the local free-carrierconcentration and mobility in semiconductor nanowires or devices with 3D-architecture.