Navy
Ships may be combined into squadrons or flotillas, which may be formed into fleets. The largest unit size may be the whole Navy or Admiralty.
A task force can be assembled using ships from different fleets for an operational task.

Personnel: Despite their acceptance in many areas of naval service, female sailors were not permitted to serve on board U.S. submarines until the U.S. Navy lifted the ban in April 2010. The major reasons historically cited by the U.S. Navy were the extended duty tours and close conditions which afford almost no privacy. The United Kingdom's Royal Navy has had similar restrictions. Australia, Canada, Norway, and Spain previously opened submarine service to women sailors.

Ranks: A navy will typically have two sets of ranks, one for enlisted personnel and one for officers.
Typical ranks for commissioned officers include the following, in ascending order (Commonwealth ranks are listed first on each line; USA ranks are listed second in those instances where they differ from Commonwealth ranks):

Midshipman / Ensign / Corvette Lieutenant
Sub Lieutenant / Lieutenant Junior Grade / Frigate Lieutenant
Lieutenant (Commonwealth & USA)/ Ship-of-the-Line Lieutenant / Captain Lieutenant
Lieutenant Commander (Commonwealth & USA)/ Corvette Captain
Commander (Commonwealth & USA)/ Frigate Captain
Captain (Commonwealth & USA)/ Ship-of-the-Line Captain
Commodore / Flotilla Admiral (in USA only: Rear Admiral (lower half))
Rear Admiral (in USA only: Rear Admiral (upper half))
Vice Admiral (Commonwealth & USA)
Admiral (Commonwealth & USA)
Admiral of the Fleet (Commonwealth) / Fleet Admiral (USA) / Grand Admiral
"Flag officers" include any rank that includes the word "admiral" (or commodore in services other than the US Navy), and are generally in command of a battle group, strike group or similar flotilla of ships, rather than a single ship or aspect of a ship. However, commodores can also be temporary or honorary positions. For example, during World War II, a Navy captain was assigned duty as a convoy commodore, which meant that he was still a captain, but in charge of all the merchant vessels in the convoy.
The most senior rank employed by a navy will tend to vary depending on the size of the navy and whether it is wartime or peacetime, for example, few people have ever held the rank of Fleet Admiral in the U.S. Navy, the chief of the Royal Australian Navy holds the rank of Vice Admiral, and the chief of the Irish Naval Service holds the rank of Commodore.

Naval infantry: Naval infantry, commonly known as marines, are a category of infantry that form part of a state's naval forces and perform roles on land and at sea, including amphibious operations, as well as other, naval roles. They also perform other tasks, including land warfare, separate from naval operations.
During the era of the Roman empire, naval forces included marine legionaries for maritime boarding actions. These were troops primarily trained in land warfare, and did not need to be skilled at handling a ship. Much later during the age of sail, a component of marines served a similar role, being ship-borne soldiers who were used either during boarding actions, as sharp-shooters, or in raids along shorelines.

The Spanish Infantería de Marina was formed in 1537, making it the oldest, current marine force in the world. The British Royal Marines combine being both a ship-based force and also being specially trained in commando frogman-style operations and tactics, operating in some cases separately from the rest of the Royal Navy. The Royal Marines also have their own special forces unit.
In the majority of countries, the marine force is an integral part of the navy but there are variations such as the French Troupes de marine which is actually part of the French Army. The United States Marine Corps is a separate armed service within the United States Department of the Navy, with its own leadership structure.

Naval aviation: Naval aviation is the application of military air power by navies, whether from warships that embark aircraft, or land bases.
In World War I several navies used floatplanes and flying boats - mainly for scouting. By World War II, aircraft carriers could carry bomber aircraft capable of attacking naval and land targets, as well as fighter aircraft for defence. Since World War II helicopters have been embarked on smaller ships in roles such as anti-submarine warfare and transport. Some navies have also operated land-based aircraft in roles such as maritime patrol and training.
Naval aviation forces primarily perform naval roles at sea. However, they are also used in a variety of other roles.

Further reading: Non-fiction:
Combat Fleets of the World: Their Ships, Aircraft and Systems - Naval Institute Press. Published annually. Comprehensive.
Braudel, Fernand, The Mediterranean in the Ancient World
Corbett, Sir Julian, Some Principles of Maritime Strategy, 1911.
Hughes Jr., Wayne P., Fleet Tactics and Coastal Combat, 1999, Naval Institute Press, ISBN 1-55750-392-3
Kennedy, Paul. The Rise and Fall of British Naval Mastery. New York: Scribner, 1976. ISBN 0-394-54674-1
Mahan, Alfred Thayer, The Influence of Sea Power upon History, 1660-1783, 1918, Little Brown, Boston.
Marder, Arthur. The Anatomy of British Seapower. New York: Octagon Books, 1940.
Marder, Arthur. "The Influence of History on Sea Power: The Royal Navy and the Lessons of 1914-1918", Pacific Historical Review. November, 1972.
Richmond, Herbert. National Policy and National Strength and other Essays. London: Longman, Green and Co., 1928.
Sprout, Harold and Margaret Sprout. Toward a New Order of Sea Power: American Naval Policy ... 1918-1922. Princeton: Princeton University Press, 1940.
Starr, Chester G., The Influence of Sea Power on Ancient History, 1989, Oxford University Press, ISBN 0-19-505666-3
Tangredi, Sam, "Globalization and Maritime Power", 2002 - National Defense University, ISBN 1-57906-060-9
Trafalgar 200 Through the Lens, ISBN 0-9553004-0-1
Wombacher, Joerg and Joerg Felfe. (2012) United We Are Strong: An Investigation into Sense of Community among Navy Crews, Armed Forces & Society, Vol. 38, No. 4
Woolley, Peter J. "The Role of Strategy in Great Power Decline", Naval War College Review. Vol. XLIX, no. 1 (1996). ISBN 1-884733-06-9
Fiction:
Alan Lewrie series by Dewey Lambdin
Aubrey–Maturin series by Patrick O'Brian
Horatio Hornblower series by C. S. Forester
Richard Bolitho series by Alexander Kent (Pseudonym of Douglas Reeman)
Tom Clancy, The Hunt for Red October, Red Storm Rising

See also: Blue-water navy
Coast guard
List of auxiliary ship classes in service
List of countries by level of military equipment
List of naval battles
List of naval ship classes in service
List of navies
List of submarine classes in service
Marines
Naval fleet
Naval militia
Naval tactics
Naval warfare
Navies of landlocked countries
Shore patrol

Notes: 

References: 

External links: 
Naval Technology - News, projects, images and white papers on the naval industry
NOSI (Naval Open Source Intelligence) - a library of world naval operational news
Navy at Scottish Military Heritage Centre
"Navy, The" . Collier's New Encyclopedia. 1921.
Hannay, David McDowall (1911). "Navy" . Encyclopædia Britannica. Vol. 19 (11th ed.). pp. 299–317.