June 4 – After arriving at Canada, the Royal Navy fleet sails out of British-controlled Halifax toward the St. Lawrence River to prepare the invasion of French Quebec. 
June 15 – The first vascular surgery in history is performed by a Dr. Hallowell (whose first name has been lost to history) at Newcastle upon Tyne, who used suture repair rather than a tying off with a ligature to repair an aneurysm on a patient's brachial artery. The case is reported in 1761 by Dr. Richard Lambert in the paper "A new technique of treating an aneurysm", published in the journal Medical Observations and Inquiries.  The new procedure of reconstructing a damaged artery replaces the practice of ligation that had risked the amputation of a limb or organ failure. 
June 26 – After the fleet finishes navigation of the St. Lawrence and arriving Île d'Orléans, British troops go ashore at France's North American territory and begin the siege of Quebec City
Madame du Coudray publishes Abrégé de l'art des accouchements (The Art of Obstetrics), and the French government authorizes her to carry her instruction "throughout the realm" and promises financial support.
^Newman, Frank G. (January 1965). "The Acquisition of a Life Insurance Company". The Business Lawyer. American Bar Association. 20 (2): 411-416. Retrieved 2016. The first life insurance company in America was organized in 1759 under the corporate title 'The Corporation for Relief of Poor and Distressed Presbyterian Ministers, and of the Poor and Distressed Widows and Children of Presbyterian Ministers'.
^ "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) p53
^Royal Observatory Greenwich souvenir guide. 2012. pp. 34-35. ISBN978-1-906367-51-0. the first precision watch and considered by many today as the most important timekeeper ever.