Specifically the late 1700s to early 1800s European ships. What were common duties performed by the maintenance crews at sea. Is there some recommended reading material on the types of tools and techniques used by the sailors to maintain a ship?
I realize this might be a broad question, so probably limit the maintenance duties to what would keep the ship in fighting shape (gun and deck maintenance etc...) , and not so much the privy/kitchen maintenance.
Maintenance fell under several headings:
Cleaning: The ship was cleaned every morning, decks swabbed and holystoned, paint work cleaned down.
Pumping: All ships leaked somewhat, worse in bad weather. Depending on how fast water came in, the pumps would need to be manned every so often to get it back out.
Coating wood: Wood lasts longer if coated with paint, varnish or oil. Most of the wood from which wooden warships were made would be coated. Coating does not last and needs to be renewed. Every day there would probably be some of the crew involved in stripping, sanding, painting, varnishing, or oiling some part of the ship.
Repairing wood: Timbers could get damaged by rot (caused by the collection of fresh water on wood) or by various stresses or impacts. Damaged wood would be cut out and new wood scarfed in by the carpenter and his mates.
Coating rigging: Almost all the rigging of these European ships was made of hemp rope. Hemp deteriorates quickly unless protected. The protection used was "parcelling" (wrapping the line with canvas), "serving" (wrapping the canvas with smaller line) and "tarring" (coating the whole parceled and served line with tar). All of the standing rigging was protected by tar, and this needed to be replaced fairly frequently. On almost all day watches, some of the watch would be engaged in tarring down the rigging.
Repairing / replacing rigging: The running rigging was generally not tarred, as this made it stiff and difficult to handle. The hemp rope used to make this rigging deteriorated (especially in intense sunlight). Running rigging had to be replaced fairly frequently. Whipping, splicing, and reaving new running rigging was a common maintenance task.
Standing rigging, protected by tar, lasted longer, but it had to be replaced eventually. The ratlines by which sailors went aloft were made of small diameter line, which did not last so long. They were also a safety hazard if they rotted and broke when men were climbing them. Replacing the ratlines was called "rattling down" and it was a fairly common maintenance task.
Making replacement standing rigging, and parceling and serving it was a fairly common maintenance task. Some of the standing rigging would be further wrapped in "baggywrinkle" to protect the sails from wear where they chafed against standing rigging. Baggywrinkle wears out fairly quickly (its job is to wear out rather than have the sails wear out), so some of the crew would often be deployed in making new baggywrinkle (made from old worn out rigging) or replacing old baggywrinkle with new.
Chipping iron: Iron, in the wet and salty conditions at sea, is very prone to rust. Almost all iron was coated with paint, to protect against rust, but moisture often got under the paint and caused rust to start. Chipping the rust off (with a "chipping hammer") and then repainting the iron was sure to employ some of the crew on every day watch. Chipping and repainting the cannon balls, was often seen as one of the most boring and unpleasant tasks at sea.
Polishing Brass: Brass has an advantage at sea over iron in that it does not rust, but it does tarnish, turning a green "verdigris" color unless polished. The brass, (binnacle, ship's bell, various portholes and hardware, sometimes some of the cannon) would be polished every day.
Repairing sails: Sail canvas (usually of flax or cotton) does not last forever. Old sails could be patched or repaired or strengthened, but also the sailmaker, his mates and some of the able seamen would usually be working on new replacement sails as well as sail repair every day.
Dry docking, Hauling or careening: Ships bottoms grow foul with weeds and barnacles. The ship worm eats holes in the underwater planks unless they are protected by various coatings. British ships were the first to cover the ships' bottoms with copper, which provides protection against marine growths, but all ships needed to renew their bottom protection (less frequently if copper plates, or more frequently if some sort of paint or coating) and clean the bottom. This usually required propping the ship upright on the hard and working at low tide (if the rise and fall of tide was enough to allow this), putting the ship in a dry dock, or "careening" the ship.
"Careening" could be done by the ship's company, if necessary, or on a long voyage or a long way from shipyards. It was a huge job, involving sending all the ship's stores and guns and ballast ashore, then hauling the ship way over on one side, to lift the bottom on the other side out of the water to be cleaned and re-protected, then hauling the ship over the other way and doing the other side, then putting all the ballast and stores and guns back on board.
That covers most of the maintenance tasks involved in looking after the ship. There were other tasks involved in maintaining the crew (getting water, stowing supplies, cooking meals, etc.), and other tasks involved in maintaining combat effectiveness (practicing with the guns, practicing sail handling and maneuvers).
Awesome answer! Full winds for you.