1728

January–March

• January 5 - The Real y Pontificia Universidad de San Gerónimo de la Habana, the oldest university in Cuba, is founded in Havana.
• January 9 - The coronation of Peter II as the Tsar of the Russian Empire takes place in Moscow.
• January 29 - The Beggar's Opera, the most popular theatrical production of the 18th century, is performed for the first time. The premiere takes place at the Lincoln's Inn Fields Theatre in London. Written by John Gay with music arranged by Johann Christoph Pepusch, the ballad opera is a satire of Italian opera.
• February 28 - Battle of Palkhed: Maratha Peshwa Bajirao I defeats the first Nizam of Hyderabad, Nizam-ul-Mulk.
• March 14 - Jean-Jacques Rousseau leaves Geneva for the first time.

April–June

• April 14 - Saint Serapion of Algiers, the first Mercedarian is canonized by Pope Benedict XIII.
• April 29 - John Essington, a member of the British House of Commons, is expelled from Commons after a successful petition to have him unseated. Essington, deep in debt, dies in Newgate Prison less than year later.
• April 30 - The 82 survivors of the wreckage of the Dutch East India Company frigate Zeewijk arrive in the new ship that they had built, Sloepie, at their original destination of Batavia in the Dutch East Indies.
• May 16 - Saint Margaret of Cortona, the patron saint of the falsely accused, homeless people and mental illness sufferers, is canonized.
• May 25 - Pope Gregory VII, who served as pontiff from 1073 to 1085, is canonized as a Roman Catholic saint.
• May 31 - The Royal Bank of Scotland invents the overdraft, allowing Edinburgh merchant William Hogg cash credit for his creditors to be paid by the bank until Hogg receives expected revenue to repay the amount owed, plus interest.
• June 14 - The Congress of Soissons opens at the French town of Soissons to negotiate a treaty between Great Britain and Spain. The treaty, which is concluded on November 9, 1729, recognizes the Spanish royal family's rule of parts of Italy, and Britain's possession of Gibraltar and Menorca.
• June 25 - The Treaty of Kyakhta is signed at the border city of Kyakhta, between Russia and China, by representatives of the Tsar Peter II, and the Emperor Yongzheng.

July–September

• July 14 - The First Kamchatka Expedition, led by Vitus Bering and his crew sail northward on the ship Archangel Gabriel from the Kamchatka Peninsula, through the Bering Strait, and round Cape Dezhnev.
• July 17 - At the age of 8, Prince Teruhito, son of Emperor Nakamikado, is named as the Crown Prince of Japan. Teruhito becomes the Emperor Sakuramachi at age 15, upon his father's death.
• July 18 - After a reign of only four months, Abdalmalik is deposed as Sultan of Morocco by his half-brother Ahmad ad Dahabi, whom he had deposed on March 13. Abdalmalik is later captured and executed on March 2, 1729.
• July 23 - At the conclusion of the Szeged witch trials in the city of the same name in Hungary, six men and six women are burned at the stake on the island of Boszorkány Sziget.
• August 16 - Because of advancing Arctic ice, the First Kamchatka Expedition turns around after Vitus Bering concludes that it had reached the easternmost point of Russia and Asia, and fails to spot the coast of Alaska because of the weather.
• August 29 - The City of Nuuk is founded in Greenland, as Fort Godt-Haab, by royal governor Claus Paarss.
• September 15 - Persian physician Mohammad Mehdi ibn Ali Naqi completes Zad al-musafirin, his treatise for travelers to Persia on preservation of their health. He notes the date as a postscript in his manual.
• September 18 - John Deane, a colonial administrator of Britain's British East [India Company], returns to Calcutta after an absence of more than two years, and takes office at Fort William to return to administering the Bengal Presidency, an area now covering the Indian state of West Bengal and the nation of Bangladesh.
• Late Summer - Voltaire ends his exile in England.

October–December

• October 20-23 - The Copenhagen Fire of 1728 burns.
• November 25 - In India, the Maratha Empire's army invades the Mughal Empire's Malwa province, crossing the Narmada River. On November 29, the two armies clash at the Battle of Amjhira; the Maratha troops, commanded by General Chimaji Appa, overcome the defenders of Malwa and Malwa's Governor Girdhar Bahadur is killed.
• December 25 - William Burnet, the British Governor of the [Province of Massachusetts Bay] since July 19, is appointed by King George II to be the Governor of the Province of New Hampshire as well, governing both future U.S. states simultaneously until September 7. Up until July, Burnet had been Governor of both New York and New Jersey since 1720.

Date unknown

• English astronomer James Bradley uses stellar aberration to calculate the speed of light, and observes nutation of the Earth's axis.