March 5 – The 1730 papal conclave to elect a new Pope for the Roman Catholic church begins with 30 Cardinals, 12 days after the death of Pope Benedict XIII. By the time his successor is elected on July 12, there are 56 Cardinals.
August 25 – French Protestant Marie Durand is imprisoned in the Tower of Constance at Aigues-Mortes for her defiance of the Roman Catholic government, and is kept captive for the next 38 years. During her incarceration, she continues to resist converting to Catholicism as a condition of release. She is finally set free on April 14, 1768 and lives 8 more years.
September 1 – A volcano erupts on Lanzarote, the easternmost of the Canary Islands and threatens the Spanish inhabitants. On Gran Canaria, the regent of the islands reports to Madrid that the flames are visible even from 130 miles (210 km) away.
November 6 – After being convicted of treason for attempting to desert the Prussian Army with Crown Prince Frederick, Hans Hermann von Katte is beheaded at the Küstrin Prison. Frederick's father, King Frederick William, forces the prince to watch the execution.
January 8 – An avalanche from the Skafjell mountain causes a massive wave in the Storfjordenfjord in Norway that sinks all boats that happen to be in the water at the time and kills people on both shores.
June 4 – The English market town of Blandford Forum is destroyed by fire, with the exception of 26 houses. About one-third of the uninsured losses are paid for by the collection of disaster relief money.
August 23 – The oldest known sports score in history is recorded in the description of a cricket match at Richmond Green in England, when the team of Thomas Chambers of Middlesex defeats the Duke of Richmond's team by 119 to 79.
September – The first successful appendectomy is performed by English surgeon William Cookesley.
Patrona Halil, an ethnic Albanian and a janissary who instigated a mass uprising in 1730 within the Ottoman Empire that brought Mahmud I to power as the new Sultan, is strangled to death in Mahmud's presence after the rebellion is finally suppressed.
March 21 – The Molasses Act is passed by British House of Commons, which reinforces the negative opinions of the British by American colonists. The Act then goes to the House of Lords, which consents to it on May 4 and it receives royal assent on May 17.
After British Prime Minister Robert Walpole's proposed excise tax bill results in rioting over the imposition of additional taxes and the use of government agents to collect them, Walpole informs the House of Commons that he will withdraw the legislation.
June 12 – In Berlin, Prince Frederick of Prussia, the 21-year-old heir to the throne reluctantly marries Duchess Elisabeth Christine of Brunswick-Bevern in order to avoid prosecution for desertion from the Prussian Army and to be guaranteed the throne. Despite the unhappy marriage Frederick and Elisabeth later reign as King and Queen Consort of Prussia.
September 12 – Stanislas Leszczynski, who had been King of Poland from 1704 to 1709 until being driven from the throne by King Augustus II, is returned to office by the vote of the Sejm. Russia and Austria protest the election, since King Stanislaus is backed by France and Sweden.
December 19 – Unsuccessful in capturing Baghdad from the Ottoman Empire, Persia's ruler Nader Shah signs the Treaty of Baghdad with the Ottoman Governor, Ahmad Khan Pasha, with the Turks and the Iranians agreeing to restore the boundary between the two empires to the lines before the 1732 Ottoman invasion of Iran.
October 31 – Chief Tomochichi of the Yamacraw band of the Muscogee Nation ends a successful four and a half month visit to Great Britain, along with Georgia Governor James Oglethorpe and other Yamacraw Indians, after having signed the cession of the area of modern day Savannah, Georgia to the Georgia Company. On June 16, he and the Muscogee delegation (Senauki, Toonahowi, Hillispilli, Umpichi, Apokutchi, Santachi and Stimaletchi) had been welcomed as guests of King George II. The group departs on HMS Aldborough after completing the visit by the largest delegation of Native Americans since 1616.
March 10 – The Russian Empire and Persia sign the Treaty of Ganja, with Russia ceding territories in the Caucasus mountains to Persia, and the two rivals forming a defensive alliance against the Ottoman Empire.
October 3 – An agreement between the European powers brings a ceasefire in the War of the Polish Succession, one week short of the second anniversary of the war. With France and Spain on the side of the reigning monarch, Stanisław Leszczyński, and Prussia, Russia, and Austria supporting Augustus III, a preliminary peace is signed that was ratified in 1738 as the Treaty of Vienna. By the terms of the treaty, Stanisław Leszczyński renounced his claim on the Polish throne and recognized Augustus III, Duke of Saxony. As compensation he received instead the duchies of Lorraine and Bar which were to pass to France upon his death.
April 14 – German adventurer Theodor Stephan Freiherr von Neuhoff is crowned King Theodore of Corsica, 25 days after his arrival on Corsica on March 20. His reign ends on November 5 when he flees the island.
September 29 – The Gin Act 1736 goes into effect, placing a steep tax on the sale of gin and license requirements for its sale, with the intent of reducing consumption of the liquor in Britain. Widely ignored, the Act is repealed in 1743. 
November 13 – Word of the discovery of silver, south of what is now the U.S.-Mexican border, reaches Sonora Governor Juan Bautista Anza and soon leads to prospectors coming to Nogales to find more silver.  Late in October, a Yaqui Indian prospector, Antonio Siraumea, had discovered large slabs of silver ("Las planchas de plata"), and at the Estancia Arizona, a ranch owned by Captain Bernardo de Urrea. The region, and later the U.S. territory, and state of Arizona are named for Urrea's ranch.
Lots are first advertised for sale in the new town of Richmond, Virginia, by the placement of a notice by William Byrd in the Virginia Gazette. According to the paper, "... on the North Side of James River, near the Uppermost Landing, and a little below the Falls, is lately laid off by Major Mayo, a Town, called Richmond, with Streets 65 Feet wide, in a pleasant and healthy Situation, and well supply'd with Springs of good Water. It lies near the Publick Warehouse at Shoccoe's, and in the midst of great Quantities of Grain, and all kind of Provisions. The Lots will be granted in Fee Simple, on Condition only of building a House in Three Years Time, of 24 by 16 Feet, fronting within 5 Feet of the Street. The Lots to be rated according to the Convenience of their Situation, and to be sold after this April General Court, by me, William Byrd."
July 10 – Thomas Pellow of Cornwall finally escapes captivity, 23 years after having been captured by Barbary pirates and held as a slave in Morocco. He arrives in British territory when the ship he is on sails into Gibraltar Bay on July 21, and later recounts his story in the book The Adventures of Thomas Pellow, of Penryn, Mariner: Three and Twenty Years in Captivity Among the Moors.
December 27 – After setting off from Rotterdam in August with 240 immigrants to America, the British ship Princess Augusta is wrecked near Block Island off of the coast of the colony of Rhode Island. During the voyage, 200 passengers and seven crew died from illness spread by contaminated water. Another 20 die after the crew leaves and rows to shore. The wreck later becomes the subject of the legend of the "Palatine Light" ghost ship and of John Greenleaf Whittier's 1867 poem "The Palatine".
China's Qing government announces that all western businessmen have to use the Cohong in Guangzhou to trade.
December 30– Months of unseasonably cold weather begin in Ireland, precipitating the Irish Famine of 1740, known as Bliain an Áir ("The Year of Slaughter"). A January 5 dispatch from Dublin to the Stamford Mercury says "Since last Wednesday we have had the most violent cold Weather that was ever known in this Kingdom; hard Frost began that evening, which has continued ever since with a very stormy Wind at South-East." At least 13% of Ireland's population dies of starvation in the year that follows.
^William H. Egle, History of the Commonwealth of Pennsylvania, Civil, Political and Military from Its Earliest Settlement to the Present Time, Including Historical Descriptions of Each County in the State, Their Towns, and Industrial Resources (E.M. Gardner Co., 1883) p322
^ abcde"Fires, Great", in The Insurance Cyclopeadia: Being an Historical Treasury of Events and Circumstances Connected with the Origin and Progress of Insurance, Cornelius Walford, ed. (C. and E. Layton, 1876) p49
^"List of British Merchant Ships, taken or plundered by the Spaniards", The Political State for the Month of April, 1738 of Great Britain (April 30, 1738) p322.
^"The imperial heritage of Peter the Great in the foreign policy of his early successors", by E. V. Anisimov, in Imperial Russian Foreign Policy, ed. by Hugh Ragsdale (Cambridge University Press, 1993) p30
^Thomas Carlyle, History of Friedrich the Second, Called Frederick the Great (Harper & Brothers, 1858) p372
^Douglas M. Gibler, International Military Alliances, 1648-2008, (SAGE Publications, 2008) p.85
^Kaveh Farrokh, Iran at War, 1500-1988 (Bloomsbury Publishing, 2011) pp110-113
^Rosse, J. Willoughby (1858). "George II". An Index of Dates, Comprehending the Principal Facts in the Chronology and History of the World, from the Earliest to the Present Time. London: Henry G. Bohn. p. 347.
^Palmer, Alan; Palmer, Veronica (1992). The Chronology of British History. London: Century Ltd. pp. 215–216. ISBN0-7126-5616-2.
^Chris Cook and Philip Broadhead, The Routledge Companion to Early Modern Europe, 1453-1763 (Taylor & Francis, 2012) p.126
^"Fires, Great", in The Insurance Cyclopeadia: Being an Historical Treasury of Events and Circumstances Connected with the Origin and Progress of Insurance, Cornelius Walford, ed. (C. and E. Layton, 1876) p50
^W. H. Wilkins, Caroline, the Illustrious Queen-Consort of George II. and Sometime Queen-Regent: A Study of Her Life and Time, Volume 2 (Longmans, Green, 1901) p20
^Oscar Peschel and Gustav Leipoldt, Physische Erdkunde: Nach den Hinterlassenen Manuscripten Oscar Peschel's (Physical Geography: According to Oscar Peschel's Surviving Manuscripts (Duncker & Humblot, 1879) p. 152
^Carlos R. Herrera, Juan Bautista de Anza: The King's Governor in New Mexico (University of Oklahoma Press, 2015) p37
^Journal du voyage fait par ordre du roi à l'équateur. Paris. 1751.
^Theorematum Quorundam ad Numeros Primos Spectantium Demonstratio.
^An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst.
^Hargreaves-Mawdsley, W. N. (1979). Eighteenth-Century Spain 1700–1788: A Political, Diplomatic and Institutional History. London: Palgrave Macmillan.
^Hassall, Arthur (1907). The Balance of Power, 1715-1789. New York: Macmillan. p. 119.
^Historical Calendar (Philippine National Historical Commission, 1970), p11
^"On the cause of the eccentricity of the woody layers which one perceives when one cuts horizontally the trunk of a tree" (De la cause de l'excentricité des couches ligneuses qu'on apperçoit quand on coupe horisontalement le tronc d'un arbre).
^ abMarley, David (1998). Wars of the Americas: A Chronology of Armed Conflict in the New World, 1492 to the Present. Santa Barbara: ABC-CLIO. p. 250.
^Commire, Anne; Klezmer, Deborah. "Lecouvreur, Adrienne (1690–1730)". Dictionary of Women Worldwide: 25,000 Women Through the Ages. Detroit: Yorkin Publications. Retrieved 4 April 2014.
^Elling, Christian (2019). Rome : the biography of her architecture from Bernini to Thorvaldsen. Place of publication not identified: Routledge. p. 109. ISBN9781000310290.
^Göransson, Elisabet (2006). Letters of a learned lady: Sophia Elisabeth Brenner's correspondence, with an edition of her letters to and from Otto Sperling the younger. Stockholm: Almqvist & Wiksell. p. 25. ISBN9789122021575.
^Hume, Robert (1988). Henry Fielding and the London theatre, 1728-1737. Oxford Oxfordshire New York: Clarendon Press Oxford University Press. p. 142. ISBN9780198128649.