Book excerpt: Topological semimetals are quantum materials that are not only extremely interesting from a theoretical point of view but also have a great potential for technological applications in which superconducting, semiconducting and other semimetal behaviors are involved. Keywords: Quantum Materials, Macroscopic Quantum Phenomena, Topological Semimetals, Dirac Semimetals, Weyl Semimetals, Nodal-Line Semimetals, Antimony and Antimonides, Antimonene, Arsenides, Bismuthides, Boron, Borides, Borophene, Carbon and Carbides, Chalcogenides, Nitrides, Phosphorus, Phosphides, Silicides, Topological Metals, Topological States of Matter.