The Catalogue of Mesozoic radiolarian genera is a revision of all described genera with re-illustration of their type species. This project was organized under the auspices of the International Association of Radiolarian Paleontologists (Inter-Rad), and was carried out by the Mesozoic Working Group. This contribution (Part 1), deals with the Triassic period only. There are 381 known Triassic radiolarian genera. Most have been published since the 1970's following the introduction of scanning electron microscopy (SEM), which enabled good pictures for most type species. For this reason the Triassic period is characterized by a very low number of nomina dubia (only 14), contrary to the higher number in the Jurassic-Cretaceous interval. The Mesozoic Working Group has carefully reviewed and reexamined the taxonomy of all available genera, their family assignment and stratigraphic ranges. Following careful comparisons, 73 genera were declared synonyms. The review has also detected 11 cases of homonymy that were duly notified to their authors, and were corrected previous to the publication of this catalogue; unfortunately one homonym still remains. Two invalid nominal genera are also reported herein. The systematic revisions have validated 282 genera for the Triassic, and of these only 30 genera cross the Triassic-Jurassic boundary At the end of the catalogue 15 additional photos are presented as support for those genera having a poor original illustration of the type species.