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1730s decade ran from January 1, 1730, to December 31, 1739.
January 29 – Anna Ivanovna ( Anna of Russia) becomes empress, following the death of her cousin, Emperor Peter II.
March 12 – John Glas is deposed from the Church of Scotland; the Glasite sect forms around him. 
April 8 – , the first Shearith Israel synagogue in New York City, is dedicated.
May 15 – Charles Townshend, 2nd Viscount Townshend, retires from his role in the government of Great Britain, leaving Robert Walpole as sole and undisputed leader of the Cabinet (i.e., prime minister). In the new Walpole ministry, Sir William Strickland, 4th Baronet, becomes Secretary at War, and Henry Pelham is Paymaster of the Forces. Spencer Compton, 1st Earl of Wilmington briefly becomes Lord Privy Seal.
May – At the urging of Sir William Gooch, the Virginia House of Burgesses passes the Tobacco Inspection Act of 1730 to regulate the quality of Virginian tobacco, and establish inspection warehouses near plantations in the Tidewater region.  The establishment of Wright's Ferry under the authority of the Province of Pennsylvania triggers Cresap's War – a nine-year-long conflict also known as the Maryland-Pennsylvania boundary dispute – the conflict mainly centers in Lancaster County, Pennsylvania and York County, Pennsylvania on either banks of the Susquehanna River.
January 25 – A fire in Brussels at the Coudenberg Palace, at the time the home of the ruling Austrian Duchess of Brabant, destroys the building, including the state records stored therein. 
March 16 – The Treaty of Vienna is signed between the Holy Roman Empire, Great Britain, the Dutch Republic and Spain.
April 1 – Battle of Dabhoi in India is fought between Sarsenapati Trimbakrao Dabhade and Bajirao Peshwa.
April 2 – The town of Raynham, Massachusetts in Bristol County is entered as a new town by the governor and court of Massachusetts, New England, America.
April 28 – A fire at White's Chocolate House, near St. James's Palace, destroys the historic club and the paintings therein, but is kept from spreading by the fast response of firemen. 
April – British trader Robert Jenkins has his ear cut off by Spanish coast guards in Cuba, for the casus belli War of Jenkins' Ear in 1739.  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 – Mikhail Gvozdev in the Sviatoi Gavriil makes the first known crossing of the Bering Strait, from Cape Dezhnev to Cape Prince of Wales in Alaska.
September 13 – The Treaty of the Three Black Eagles or the Treaty of Berlin, a secret treaty between the Austrian Empire, the Russian Empire and Prussia against Polish-Lithuanian Commonwealth.
September 16 – The magnitude 5.8 Montreal earthquake occurs in Montreal, Quebec, Canada.
November 29 – The magnitude 6.6 Irpinia earthquake causes 1,940 deaths in the former Kingdom of Naples, southern Italy.
December 7 – The original Theatre Royal, Covent Garden, London (the modern-day Royal Opera House) is opened. December – 139 members of the Parlement of Paris, exiled by order of King Louis XV, secure their recall.
January 8 – Salzburgers, Lutherans who were expelled by the Roman Catholic Bishop of Salzburg, Austria, in October 1731, set sail for the British Colony of Georgia, in America. 
March 12 – Salzburgers arrive at the mouth of the Savannah River, in the British Colony of Georgia.
April 25 – Easter occurs on the latest possible date (the next time is in 1886).
June 17 – French troops take Philippsburg, but Duke of Berwick is killed.
June 21 – In Montreal, New France, a black slave known by the French name of Marie-Joseph Angélique is tortured then hanged by the French authorities for allegedly setting a fire that destroyed part of the city. June 30 – War of the Polish Succession: Russian troops take Gda?sk ( German: Danzig), which had been besieged since February 1734, after the failure of a French expedition to relieve the city.
January 23 – The Civil Code of 1734 is passed in Sweden.
January 26 – Stanislaus I of Poland abdicates his throne.
February 12 – Francis I, Holy Roman Emperor marries Maria Theresa of Austria, ruler of the Habsburg Empire.
April – The Genbun era begins in Japan. The era of Ky?h? Reforms ends.
March 8 – Nader Shah, founder of the Afsharid Dynasty, is crowned Shah of Iran.
March 31 – Bellevue Hospital was founded.
April 14 – The Porteous Riots erupt in Edinburgh, after the execution of smuggler Andrew Wilson, when town guard Captain John Porteous orders his men to fire at the crowd. Porteous is arrested later.
May 8 – Frederick, Prince of Wales, marries Princess Augusta of Saxe-Gotha.
May 26 – Battle of Ackia: British and Chickasaw Native Americans defeat French troops.
June 8 – Leonhard Euler writes to James Stirling, describing the Euler-Maclaurin formula, providing a connection between integrals and sums. June 19 – A French Academy of Sciences expedition, led by Pierre Louis Maupertuis, with Anders Celsius, begins work on measuring a meridian arc in Meänmaa, Finland. 
Neustrelitz becomes the capital of Mecklenburg-Strelitz.
Bushehr is founded in Persia. The
Belgrade Fortress is completed.
George Hamilton, 1st Earl of Orkney, becomes the first Field Marshal of Great Britain. A fire in the Russian city of
Saint Petersburg burns 2,000 houses. A fire in
Stony Stratford, England consumes 53 houses. One of the earliest records of use of a
bathing machine is made at Scarborough, England.
Charles Marie de La Condamine, with François Fresneau Gataudière, makes the first scientific observations of rubber, in Ecuador. 
Leonhard Euler produces the first published proof of Fermat's "little theorem."  Sir
Isaac Newton's (1671), describing his method of Method of Fluxions differential calculus, is first published (posthumously) and Thomas Bayes publishes a defense of its logical foundations (anonymously). 
Muhammad ibn Abd al-Wahhab writes the Kitab at-tawhidt, marking the beginning of Wahhabism. The Haidamakas raid the shtetl of Pavoloch, killing 35.
July – Austria enters the Russo-Turkish War.
September 1 – The oldest existing English language newspaper in the world, , is founded in The News Letter Belfast, Ireland.
September 20 – Runner Edward Marshall completes his journey in the Walking Purchase, forcing the cession of 1,200,000 acres (4,900 km 2) of Lenape-Delaware tribal land to the Pennsylvania Colony.
October – The first national stage in Sweden opens, when the play Den svenska sprätthöken is performed in the native language, by the first native actors, on the stage of in Bollhuset Stockholm.
October 7 – A tropical cyclone strikes Bengal, India, killing approximately 300,000.
October 16 – An earthquake with an estimated magnitude of 9.3 occurs off the shore of Russia's Kamchatka Peninsula. Tsunamis up to 60 metres (200 ft) high follow in the Pacific ocean.  November 4 – The , the oldest working Teatro di San Carlo opera house in Europe, is inaugurated in Naples, Italy.
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