Well-trained corps of naval officers.

In 1805, the First French Empire, under Napoleon Bonaparte, was the dominant military land power on the European continent, while the Royal Navy controlled the seas.^[3] During the course of the war, the British imposed a naval blockade on France, which affected trade and kept the French from fully mobilising their own naval resources.^[4] Despite several successful evasions of the blockade by the French navy, it failed to inflict a major defeat upon the British, who were able to attack French interests at home and abroad with relative ease.^[5]
When the Third Coalition declared war on France, after the short-lived Peace of Amiens, Napoleon was determined to invade Britain. To do so, he needed to ensure that the Royal Navy would be unable to disrupt the invasion flotilla, which would require control of the English Channel.^[6]
The main French fleets were at Brest in Brittany and at Toulon on the Mediterranean coast. Other ports on the French Atlantic coast harboured smaller squadrons. France and Spain were allied, so the Spanish fleet based in Cádiz and Ferrol was also available.^[7]
The British possessed an experienced and well-trained corps of naval officers.^[8] By contrast, some of the best officers in the French navy had either been executed or had left the service during the early part of the French Revolution.^[9] Vice-Admiral Pierre-Charles Villeneuve had taken command of the French Mediterranean fleet following the death of Latouche Treville. There had been more competent officers but they had either been employed elsewhere or had fallen from Napoleon's favour.^[10] Villeneuve had shown a distinct lack of enthusiasm for facing Nelson and the Royal Navy after the French defeat at the Battle of the Nile in 1798.^[11]
Napoleon's naval plan in 1805 was for the French and Spanish fleets in the Mediterranean and Cádiz to break through the blockade and join forces in the Caribbean. They would then return, assist the fleet in Brest to emerge from the blockade, and together clear the English Channel of Royal Navy ships, ensuring a safe passage for the invasion barges.^[12]

The Caribbean

Early in 1805, Vice Admiral Lord Nelson commanded the British fleet blockading Toulon. Unlike William Cornwallis, who maintained a tight grip off Brest with the Channel Fleet, Nelson adopted a loose blockade in the hope of luring the French out for a major battle.^[12] However, Villeneuve's fleet successfully evaded Nelson's when the British were blown off station by storms. While Nelson was searching the Mediterranean for him, erroneously supposing that Villeneuve intended to make for Egypt, Villeneuve passed through the Strait of Gibraltar, rendezvoused with the Spanish fleet, and sailed as planned for the Caribbean. Once Nelson realised that the French had crossed the Atlantic Ocean, he set off in pursuit.^[13]

Cádiz

Villeneuve returned from the Caribbean to Europe, intending to break the blockade at Brest,^[11] but after two of his Spanish ships were captured during the Battle of Cape Finisterre by a squadron under Vice-Admiral Sir Robert Calder, Villeneuve abandoned this plan and sailed back to Ferrol in northern Spain.^[14] There he received orders from Napoleon to return to Brest according to the main plan.^[15]
Napoleon's invasion plans for Britain depended on having a sufficiently large number of ships-of-the-line before Boulogne in France. This would require Villeneuve's force of 33 ships to join Vice-Admiral Ganteaume's force of 21 ships at Brest, along with a squadron of five ships under Captain Allemand, which would have given him a combined force of 59 ships-of-the-line.
When Villeneuve set sail from Ferrol on 10 August, he was under orders from Napoleon to sail northward toward Brest. Instead, he worried that the British were observing his manoeuvres, so on 11 August he sailed southward towards Cádiz on the southwestern coast of Spain.^[16] With no sign of Villeneuve's fleet, on 25 August, the three French army corps' invasion force near Boulogne broke camp and marched into Germany, where it was later engaged.^[17][18]
The same month, Nelson returned home to Britain after two years of duty at sea.^[19] He remained ashore for 25 days and was warmly received by his countrymen.^[20] Word reached Britain on 2 September about the combined French and Spanish fleet in Cádiz harbour.^[21] Nelson had to wait until 15 September before his ship, HMS Victory, was ready to sail.^[22]
On 15 August, Cornwallis decided to detach 20 ships-of-the-line from the fleet guarding the English Channel and to have them sail southward to engage the enemy forces in Spain.^[23] This left the Channel drastically reduced of large vessels, with only 11 ships-of-the-line present.^[24] This detached force formed the nucleus of the British fleet that would fight at Trafalgar. This fleet, under the command of Vice-Admiral Calder, reached Cádiz on 15 September. Nelson joined the fleet on 28 September to take command.^[25]
The British fleet used frigates (faster, but too fragile for the line of battle), to keep a constant watch on the harbour, while the main force remained out of sight, approximately 50 miles (80 km) west of the shore.^[26] Nelson's hope was to lure the combined Franco-Spanish force out and engage it in a decisive battle. The force watching the harbour was led by Captain Blackwood, commanding HMS Euryalus.^[26] He was brought up to a strength of seven ships (five frigates and two schooners) on 8 October.