January 18 – The Dutch East India Company cargo ship Fortuyn, on its maiden voyage, departs from the Cape of Good Hope in South Africa after a layover of 16 days following its arrival from the Netherlands. With a crew of 225 commanded by Pieter Westrik, the ship departs for Batavia in the Dutch East Indies and is never seen again.
March 7 – Pope Innocent XIII dies at the age of 68 after less than three years as the Roman Catholic pontiff.
March 20 – The 1724 papal conclave opens in Rome, 13 days after the death of Innocent XIII. Starting with 33 electors and eventually having 53, the conclave deliberates for more than two months before selecting a successor.
April–June
April 7 – (Good Friday) Bach leads the first performance of his St John Passion,""carefully designed with a great deal of musico-theological intent", on Good Friday.
April 28 – The first of the seven Drapier's Letters, satirical pamphlets seeking to arouse public opinion in Ireland against the imposition by the British of a privately minted copper coinage, is published by Jonathan Swift, Dean of St Patrick's Cathedral, Dublin and author, writing under the pseudonym "M. B., Drapier", identifying himself as a drapier or seller of cloth.
May 13 – Cardinal Giulio Piazza, the Archbishop of Faenza, comes within four votes of being elected the new Pope
May 29 – Cardinal Vincenzo Orsini, the Archbishop of Benevento, accepts the papacy, two days after being unanimously selected by the cardinals at the papal conclave in Rome. He becomes the 245th pontiff as Pope Benedict XIII.
September 4 – José de Grimaldo, who had been Prime Minister for Spain's King Philip V until the latter's abdication in January, resumes office with the return of King Philip.
September 24 – The Paris Bourse, the stock exchange for France, is created by order of King Louis XV on the advice of Nicolas Ravot d'Ombreval, four years after a financial panic had shut down trading. Stock markets had already been set up in Lyon, Bourdeaux and Toulouse.
December 2 – The Metropolitan Mojsije Petrović, leader of the Serbian Orthodox Church within the Habsburg monarchy, issues a 57-point decree to purge the church of the Turkish influence.
By order of the Nizam, Hyderabad is made the permanent capital of the Indian princely state of the same name. It becomes capital of the Indian states of Telangana and Andhra Pradesh
December 14 – The Viceroyalty of Zhili (modern-day Hebei province) is recreated in the Chinese Empire by the Emperor Yongzheng for the first time in 55 years, with Li Weijun as the first Viceory. Zhili exists as a viceroyalty until the fall of the Qing dynasty in 1912.
December 24 – Francesco Valesio resumes writing his Diario di Roma, 13 years after he ceased his recording of daily life in Rome.
^Najita, Tetsuo (1987). Visions of virtue in Tokugawa Japan : the Kaitokudō Merchant Academy of Osaka. Chicago: University of Chicago Press.
^Torres, João Romano. "Vilas Boas (D. frei Manuel do Cenáculo)". Portugal - Dicionário Histórico, Corográfico, Heráldico, Biográfico, Bibliográfico, Numismático e Artístico, Volume VII (in Portuguese). Retrieved November 15, 2020.