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The present collection of articles focuses on different aspects of topological-materials studies. Recent progress in both, theoretical and experimental, studies is covered in this Special Issue. A particular stress is given on different optical investigations, as well as on recent band-structure calculations. Besides, neutron scattering experiments, crystal growth, and a number of theoretical models for different topological systems are discussed.

topological insulators --- optical conductivity --- Dirac materials --- Weyl nodes --- screw rotation symmetry --- line node --- space group 19 --- space group 61 --- cyclotron resonance --- crystal growth --- optical floating zone method --- SmB6 --- Sm1-xCexB6 --- topological insulator --- kondo insulator --- topology --- chirality --- multifold semimetal --- optics --- DFT --- topological semimetal --- cobalt monosilicide --- mechanical deformation --- quantum anomalous Hall effect --- Faraday rotation --- terahertz spectroscopy --- inelastic neutron scattering --- topological materials --- anomalous Hall effect --- isotropic ferromagnet --- kagome --- frustrated magnetism --- skyrmion --- magnetization --- optical-conductivity scaling --- topological semimetals --- band structures --- high Chern numbers --- bulk-edge correspondence --- Weyl semimetals --- band-structure calculations --- optical response --- n/a