A topsail is a sail set above another sail; on square-rigged vessels further sails may be set above topsails.
Square rig 
On a square rigged vessel, a topsail is a square sail rigged above the course sail and below the topgallant sail where carried. A full rigged ship has either single or double ("split" upper and lower) topsails on all masts, the single or lower topsail being the second sail above the deck and the upper topsail where so rigged being the third.
Although described as a "square" sail, this term refers not to a sail's shape but to it and its yard being rigged square to the keel of the vessel rather than in line with it or "fore and aft"; the topsail was and is always trapezoidal, the lengths of the upper yards being progressively smaller the higher they are. The bottom edge (foot) of the topsail, like that of other square sails, is slightly concave, .
Although topsails of a kind were used at least as early as Roman times, they first came into use in Europe some time in the 15th century. Initially small and carried only on main and fore masts, they gradually increased in size and importance until by the middle of the 17th century and were the principal and largest sails of the ship, the first sails to be set and the last to be taken in. It was quite common for a ship to sail with topsails and jibs alone; the position of the topsails well above the sea ensured that they received a steady breeze even if the seas were rough.
The larger topsails were difficult and dangerous to handle in strong winds. Sometime in the 1680s, reef-bands were introduced to tie up part of the sail, with topsails eventually getting four of these, and reefing the sails became a regular occupation of sailors. In the mid 19th century, topsails of merchant vessels were split into separate upper and lower topsails that could be managed separately and far more easily by smaller crews.
Gaff rig 
Gaff topsails, like gaff rigs in general, may still be seen today but were once more common. The gaff rig has been largely superseded by the bermuda rig, which has no topsails. On a gaff rigged sailing boat, topsails may take a few different forms:
A yard topsail are similar, but set on a yard. Early 19th century topsail yards were set almost horizontally, but gradually increased in angle until the became almost vertical extension of the topmast.
A jack-yard topsail (or Club topsail) instead has its lower edge (or foot) extended out beyond the end of the gaff with a short yard, called a "jack-yard". A jack-yard topsail may also have the aforementioned vertical yard, although this makes for a very large topsail.
A cornish topsail is a triangular sail having it's luff extended well above the masthead by being laced to a yard hoisted by a halyard rove through a sheave fitted diagonally in the mast. The heel of the yard fits immediately about the gaff and is kept in place by a tackline called a timminoggy.
A square topsail is a square-rigged sail, generally carried above the foresail only, on gaff schooners. Gaff-rigged vessels carrying square tops are referred to as "square-topsail sloops", "square-topsail schooners", etc. Occasionally this is shortened to simply "topsail sloop" or "topsail schooner", although this term can apply to vessels carrying topsails of any kind.
A raffee is a square-rigged topsail which is triangular in shape.
Other uses 
On rigs having multiple jibs or staysails of which at least one is set high, such as many late 19th and 20th Century racing cutters, the uppermost of these, set flying or on a topmast stay, is often called the jib topsail.
- Leather, John (2001). The Gaff Rig Handbook (second ed.). Woodenboat Books. p. 54. ISBN 0-937822-67-1.
- Leather, John (2001). The Gaff Rig Handbook (second ed.). Woodenboat Books. p. 56. ISBN 0-937822-67-1.
- Leather, John (2001). The Gaff Rig Handbook (second ed.). Woodenboat Books. p. 58. ISBN 0-937822-67-1.
- Leather, John (2001). The Gaff Rig Handbook (second ed.). Woodenboat Books. p. 59. ISBN 0-937822-67-1.
- Casson, Lionel (1995): "Ships and Seamanship in the Ancient World", Johns Hopkins University Press, ISBN 978-0-8018-5130-8, pp. 240–241
- John Harland & Mark Myers, Seamanship in the Age of Sail; Lees "Masting & Rigging"; "The Young Sea-Officer's Sheet Anchor"