J. R. R. Tolkien invented a number of calendars for his fantasy-world of Middle-earth. Middle-earth is set on the Earth in a fictional prehistoric era, so a year is the same length as our year. Appendix D of Tolkien's The Lord of the Rings (published 1955) gives details of his invented calendars.
One of these is the Shire Calendar used by his fictional Hobbits of the Shire. The calendar is closely based on the historical Anglo-Saxon calendar reported by Bede.
The same appendix gives more information on the Shire Calendar's background in the fictional history of Middle-earth, stating that the Shire Reckoning is a conservative continuation of the calendar of Númenór as used in Middle-earth during the Second Age, but revised in the Third Age by Mardil and Hador, the first and seventh ruling Stewards of Gondor. The Hobbits retained the unreformed King's Reckoning, but introduced a reform that resulted in a fixed number of weeks (in imitation of the historical 10th-century Icelandic calendar).
Appendix D further gives some information on the Reckoning of Rivendell, the calendar used by the Elves in Imladris (Rivendell), which divided the solar year into six "seasons" or "long months". The only allusion to a calendar of the Dwarves is made in The Hobbit, regarding the "dwarves' New Year" or Durin's Day.