The Royal Tierran Navy is very much the senior branch of the Tierran armed forces. They're very much influenced by the British Royal Navy of the Napoleonic Wars. It's mostly composed of two formations, aside from a reserve force in Aetoria itself: "Northern Fleet", based in the naval base at Northern Pillars, and "Southern Fleet" based in the city of Havenport.
Northern Fleet is larger than the Southern Fleet, with more of the heavier ships-of-the-line. All in all, the Navy as a whole fields about three dozen ships-of-the-line mounting anywhere from 98 to 56 guns. In addition, there are another four dozen or so frigates of 52-26 guns, usually used to screen the battle line in fleet engagements or act as commerce raiders and interceptors. Lastly, the Navy has about sixty lighter ships: brigs and sloops of less than 24 guns, used for anti-piracy patrol, hunting down smugglers and supply runs to isolated outposts.
To give you a idea of the amount of manpower and resources the fleet costs to maintain: The crew of a 44 gun frigate usually adds up to about 400 men including a dozen commissioned officers, two dozen petty officers, about three hundred seamen and a company of marines (who have their own officers, and are technically part of the Royal Army's hierarchy). Naturally, the fleet is an immense drain on manpower: the Royal Tierran Navy has a wartime strength of well over 65 000 men, not counting four full regiments of marines.
The Navy is headed, ceremonially, by the "Admiral-Royal", who, as you may have guessed, happens to be the King. In reality, the Navy is commanded, informally, by the Port Admiral at Aetoria, who in turn reports to the Minister of War, on the King's Privy Council. The three Port Admirals (Aetoria, Northern Pillars and Havenport) are effectively allowed to operate independently, short of imperative orders from His Majesty's Government.
Ranks are as follows:
Petty Officer -Junior (In charge of guns and work crews)
Petty Officer -Senior
Warrant Officer (Sailing Masters, Pursers)
Midshipman (Adolescent officers-in-training)
Lieutenant -Commanding (Lieutenants in command of small vessels like sloops-of-war)
Post Captain (In command of full ships, but not confirmed to the Captain's List)
Captain of the List (Appointment approved by the Minister of War)
Commodore -Rear Admiral (Squadron command)
Vice Admiral (In command of one of the three fleets)
Admiral (In command of the ports where each of the three fleets is based in.)
Admiral-Royal (The King)