When Adam Smith was 17, Britain was at war against Spain, ostensibly due to an old grievance of a Captain Robert Jenkins. His merchant ship was boarded by Spanish coast guards and Jenkins had his ear sliced off by one of the coast guards.
Great Britain against Spain

December 1740 to 11th June 1742

This incident was used to justify war, but really it was about improving trade conditions coercing the Spanish to pressure Spain not to renege on the lucrative asiento contract, which gave British slavers permission to sell slaves in Spanish America.

Great Britain were again at war with France 

Summer 1745 to 16th April 1746

Jacobite Uprising (The Forty-Five)

Great Britain against Jacobites, France

July 1746 to 24th April 1748

French and Indian War (Became Part of the Seven Years War)

Great Britain against France

Summer 1756 to 10th February 1763

CARNATIC WARS

Great Britain against France, Mughal Empire (The Mughal empire extended over large parts of the Indian subcontinent and Afghanistan. The empire was the second largest to have existed in the Indian subcontinent, spanning 4 million square kilometres at its zenith, after the Maurya Empire, which spanned 5 million square kilometres.)  

The conflicts involved numerous nominally independent rulers and their vassals, struggles for succession and territory, and included a diplomatic and military struggle between the French East India Company and the British East India Company. They were mainly fought on the territories in India which were dominated by the Nizam of Hyderabad up to the Godavari delta. As a result of these military contests, the British East India Company established its dominance among the European trading companies within India. The French company was pushed to a corner and was confined primarily to Pondichéry. The East India company’s dominance eventually led to control by the British Company over most of India and eventually to the establishment of the British Raj.

First Carnatic War (In the 18th century, the coastal Carnatic region was a dependency of Hyderabad) 1746 – 1748

Second Carnatic War

Great Britain against France, Mughal Empire

Summer 1748 to 1754

Third Carnatic War

Great Britain against Mughal Empire

May 1754 to 10th February 1763

First Silesian War (Part of the War of Austrian Succession)

Hapsburg Empire against Prussia

1741 to 10th July 1747

Second Silesian War (Part of the War of Austrian Succession)

Hapsburg Empire against Prussia

May 1744 to 24th April 1748

The first two can be viewed in the context of the larger War of the Austrian Succession, while the “Third Silesian War” is better known as the Seven Years’ War. Silesia was strategically important to Prussia because “it significantly blunted the capacity of Prussia’s two chief foes—Austria and Russia—to meddle in Prussian affairs”.[1] Prussian victory (and possession of Silesia) foreshadowed a wider struggle for control over the German-speaking peoples that would culminate in the Austro-Prussian War of 1866.

Seven Years War (Third Silesian War)

Prussia, Hanover, Great Britain, Brunswick against France, Austria, Russia, Spain, Sweden, Saxony, Mughal Empire

Italian Campaigns (Part of the War of Austrian Succession)

Spain, Naples, France against Hapsburg Empire, Prussia

April 1744 to 25th December 1745

King George’s War (Part of the War of Austrian Succession)

Great Britain against France

Summer 1745 to 16th April 1746

Seven Years War (Third Silesian War)
Prussia, Hanover, Great Britain, Brunswick against France, Austria, Russia, Spain, Sweden, Saxony, Mughal Empire

17th September 1757 to 22nd May 1762

Pomeranian War (Part of the Seven Years War)

Prussia against Sweden

7th December 1758 to 10th February 1763

American Revolutionary War (American War of Independence)

United States, France, Spain against Great Britain

Spring 1787 to January 1792

French Revolution

French Royalists against French Republicans

17th April 1792 to October 1797

War of the First Coalition (French Revolutionary Wars) (Precursor to the Napoleonic Wars)

France against Austria, Prussia, Great Britain, France, Spain, Portugal, Sardinia, Naples, Sicily