The Nile

Background

In May 1797 Napoleon, the best-known but still just one of several French generals, took ship from Toulon with an army bound for Egypt, escorted by Admiral Brueys with 13 sail of the line. Warned of the assembly at Toulon, but unaware of its destination, St Vincent, influenced by a heavy hint from the Admiralty, sent Rear-Admiral Nelson with three of the line and two frigates into the Mediterranean to reconnoitre: shortly after he reinforced him with ten more of the line under Troubridge as commodore.
Nelson learned that in June the French had taken Malta and then sailed again. He guessed for Alexandria, and sent the sloop Mutine (16) to Alexandria as a scout. Mutine reached Alexandria one day before the French arrived, and sailed back again without seeing them; as a result Nelson spent three weeks ranging the Mediterranean without finding the French fleet, while Napoleon's army conquered Egypt.
Brueys' fleet was left at anchor at Aboukir Bay, his flagship L'Orient being too big to enter Alexandria harbour, and had been there for three weeks when finally Nelson found it on July 29th. While the two fleets were matched in numbers, Brueys had a slight edge in size: Nelson had thirteen 74-gun ships and the 50-gun Leander, while Brueys' flagship mounted 120 guns and he had two 80- gun vessels as well as nine 74s, plus four frigates, two sloops and three bomb vessels. However, the French fleet was at anchor, the thirteen of the line moored in line ahead, the shore being to port, with the four frigates inside them, significantly so since it was an indication to Nelson of the depth of water available inside the French line.
A further indicator was that the French ships were at single anchor, which meant they had been left free to swing with the wind (a ship at single anchor always points into the wind), which meant in turn that there must be enough water inside them to float a 74.

The battle (29-30 July 1798)

The shore, and therefore the line of the French fleet, ran at this point roughly north north-west, and as the British came in sight in the early evening, the wind was also north north-west: the French line were facing directly into it. Brueys assumed the British would wait till morning before beginning the battle, but Nelson moved immediately into action, coming towards the French from the north-east with the wind slight behind the starboard beam.
At the head of the British line, Troubridge's Culloden hit a reef, and though rescued later, played no part in the action. That left Orion to be the first British ship to come up to the French, sailing inside the French line and down to engage Peuple Souverain, the fifth ship in the line. Behind her Theseus, Audacious and Zealous also sailed between the French and the shore (though outside the line of the French frigates: one of these, Sérieux, opened fire, but was sunk by Orion without much ado). Nelson's Vanguard then sailed down the outside of the French, followed by Minotaur and Defence, pitting eight British ships against the leading French five, which happened to be the oldest and weakest French ships. All of the French line were taken by surprise by the inshore attack in the dark: their landward batteries were unprepared, without even their guns run out on that side when the action started.
Meanwhile, Bellerophon bypassed the British ships already in action on the seaward side, and took on the French flagship L'Orient in an unequal battle, while Majestic went past her to engage Tonnant. The first French ship driven out of the line was Peuple Souverain, with Orion inside her and Defence outside. The gap thus left was taken up by the little Leander, making up for her relatively puny broadside by being in position to rake Franklin across the bows. L'Orient's far heavier broadside dismasted and severly damaged Bellerophon, but her place was more than filled by the last two British ships to enter the action, Swiftsure and Alexander. At 9 o'clock L'Orient was seen to be on fire, and at 10 o'clock she blew up with an explosion so immense that all firing stopped for ten minutes.
By midnight all of the leading seven French ships were out of the action one way or another. Of the remainder, only Tonnant, eighth in line, was engaged: by 3 a.m. she was dismasted, and the British could turn their attention to the rearmost ships while waiting for her to surrender, as she eventually did. Heureux and Mercure, the next in line were attacked and forced to strike, and the rearmost, Timoleon, ran aground, where she was set on fire by her crew. The remaining two ships, Généreux and Guillaume Tell, relatively undamaged, were able to escape with two frigates.
Despite the damage to Bellerophon and the grounding of Culloden, no British ship was lost. On the other side the French lost one blown up, one burnt, one wrecked and nine surrendered, in what may well have been the most overwhelming naval defeat (in a single engagement) of all time.

Aftermath

This was Nelson's first battle in overall command, and it is distinguished from all other previous battles of the war - indeed for several centuries - not so much by its tactics, unorthodox and brilliant as they were but by the way in which Nelson's objective became not merely the winning of the battle but the destruction of the enemy fleet.
Even Duncan at Camperdown, which had perhaps come closest to this aim, had allowed eleven ships to escape: it wasn't until the Helder, the year after the Nile, that Duncan moved in to destroy the rest. Nelson had changed the meaning of a naval battle, just as Napoleon in a similar way had changed the meaning of a military battle (or, perhaps, to make it again what it had been in the days of the Romans).
From the point of view of the immediate war situation, the result of the battle was not as great as it might have been. It is true that the Nile marked the triumphant re-entry of the British fleet into the Mediterranean, from which it would never again be dislodged by force, though a base still had to be won. On the other hand, Napoleon still held Egypt, and his army there was still a threat to India.
And most importantly of all from the point of the war as a whole, the battle had come too late. If there is a parallel universe in which Nelson failed at the Nile, its history might not be very different from our own. But had Nelson found the French fleet on the way to Egypt, Napoleon would very probably have been taken or killed: that would have changed subsequent history totally.
Napoleon subsequently slipped back through the Mediterranean, despite the British fleet, in the frigate Muiron, in just such a way, ironically enough,as Nelson had slipped through the Spanish fleet in 1796. For the moment, both their lives were charmed.
For his victory, Nelson became a peer: a more important personal result however may have been that he took Vanguard to Naples for repairs, there meeting Sir Charles and Lady Hamilton. Presumably without prescience St Vincent wrote to him from Cadiz: "Tell Lady Hamilton I rely on her to administer to your health."

Note

Bolitho was apparently at the Nile, though the battle is not recorded in any of the Bolitho books (so far). However, his squadron's interception of some of the French fleet on the way to Egypt weakened it.