The year 1637 in literature involved some significant events.

Events

• Hamlet is performed before King Charles I and Queen Henrietta Maria at Hampton Court Palace on January 24.
• On October 2, the London theatres re-open; they had been closed almost continuously since May 1636, due to a severe outbreak of bubonic plague.
• The King's Men mount a production for the Court of William Cartwright's The Royal Slave, a play that was first staged at Christ Church, Oxford the previous year. The company is paid an extra £30 "for their pains in studying and acting" the drama.

New books

• René Descartes - Discours de la Méthode
• Thomas Heywood - Pleasant Dialogues and Dramas
• Marin Mersenne - Universal Harmony
• María de Zayas y Sotomayor - Novelas amorosas y ejemplares
• Five plays by James Shirley are published in individual editions - The Example, The Gamester, Hyde Park, The Lady of Pleasure, and The Young Admiral

New drama

• Pedro Calderón de la Barca - El Tetrarca published
• John Fletcher and Philip Massinger - The Elder Brother published.
• François Tristan l'Hermite - Penthée
• Thomas Heywood - The Royal King and the Loyal Subject published
• John Milton - Comus (masque) published
• Thomas Nabbes - Microcosmus, a Moral Masque
• Thomas Neale - The Warde
• Joseph Rutter - The Cid, Part 1 published
• James Shirley - five plays published in five single-play quartos: The Example, The Gamester, Hyde Park, The Lady of Pleasure, and The Young Admiral
• Sir John Suckling - Aglaura
• George Wilde - The Converted Robber

Poetry

• William Alexander, 1st Earl of Stirling - Recreations of the Muses
• James Day - A New Spring of Divine Poetry
• Thomas Jordan - Poetical Varieties
• Shackerley Marmion - Cupid and Psyche, a 2000-line translation and adaptation of The Golden Ass of Apuleius

Births

• December 24 - Pierre Jurieu, Protestant theologian (died 1713)
• December 30 - William Cave, theologian (died 1713)
• date unknown - Zeb-un-Nisa, Sufi poet (died 1702)
• probable - Robert Ferguson, pamphleteer (died 1714)

Deaths

• February - Gervase Markham, poet (born c.1568)
• February 24 - Dominicus Arumaeus, Dutch legal writer (born 1579)
• March 19 - Péter Pázmány, Hungarian philosopher and theologian (born 1570)
• May 19 - Isaac Beeckman, philosopher and diarist (born 1588)
• August 6 - Ben Jonson, poet and dramatist (born c.1572)
• August 10 - Johann Gerhard, Lutheran theologian (born 1582)
• October 5 - Daniel Cramer, Lutheran theologian and dramatist (born 1568)