The classical guitar (also called classic guitar, Spanish guitar, nylon-string guitar or concert guitar) is a 6-stringed plucked string instrument from the family of instruments called chordophones. The classical guitar is well known for its comprehensive right hand technique, which allows the soloist to perform complex melodic and polyphonic material, in much the same manner as the piano.
The phrase "classical guitar" is ambiguous in that it might refer at least three different concepts:
the instrumental technique — the individual strings are usually plucked with the fingernails or rarely without nails.
its historic repertoire — though this is of lesser importance, since any repertoire can be (and is) played on the classical guitar (additionally: classical guitarists are known to borrow from the repertoires of a wide variety of instruments)
its shape, construction and material excluding three strings made of nylon — modern classical guitar shape, or historic classical guitar shapes (e.g. early romantic guitars from France and Italy). A guitar family tree can be identified. (The flamenco guitar is derived from the modern classical, but has differences in material, construction and sound)
The name classical guitar does not mean that only classical repertoire is performed on it, although classical music is a part of the instrument's core repertoire (due to the guitar's long history); instead all kinds of music (folk, jazz, flamenco, etc.) are performed on it.
The term modern classical guitar is sometimes used to distinguish the classical guitar from older forms of guitar, which are in their broadest sense also called classical, or more descriptively: early guitars. Examples of early guitars include the 6-string early romantic guitar (ca. 1790 - 1880), and the earlier baroque guitars with 5 courses.
Today's modern classical guitar was established by the late designs of the 19th century Spanish luthier Antonio Torres Jurado. Hence the modern classical guitar is sometimes called the "Spanish guitar".
The classical guitar has a long history and one is able to distinguish various:
repertoire (composers and their compositions, arrangements, improvisations)
Both instrument and repertoire can be viewed from a combination of various contexts:
historical (chronological period of time)
baroque guitar — 17th to mid 18th century
early romantic guitars — 19th century (for music from the Classical and Romantic periods)
modern classical guitars
e.g. in the 19th century: Spanish guitars (Torres), and French guitars (René Lacôte, ...), etc.
cultural/stylistic and social aspects
e.g. baroque court music, 19th century opera and its influences, 19th century folk songs, Latin American music, etc.
Brief examples using the above classifications (historical, cultural/stylistic, social etc.), to show the colourful diversity of the classical guitar:
Robert de Visée (ca. 1650--1725) with French Court music for baroque guitar and lute. He was the guitar player (maître de guitare du Roy) of Louis XIV of France at the court of Versailles. His works are influenced by hearing Jean-Baptiste de Lully (1632--1687) who was also engaged at the court of Louis XIV.
Mauro Giuliani (1781--1829) with Italian/Viennese classical music for the 19th century so-called early romantic guitar. He was chamber-virtuoso of Archduchess Marie Louise of Austria. Some of his works include strong influences from his visits to 19th century opera performances.
Francisco Tárrega (1852--1909) of Spain. His intimate salon-style music is both romantic in character and includes charming character pieces such as polkas and waltzes. He even played for the Queen of Spain, Isabel II. From 1869, Tárrega used a guitar by Antonio de Torres (1817--1892).
Agustín Barrios (1885--1944) from Paraguay, towards the end of his life using a modern classical guitar. His music is romantic in style, with some works showing strong folkloric Paraguayan influences, shaped from his cultural background.
Sergei Orekhov (Сергей Орехов) (1935--1998) with music for the Russian 7-string guitar. In his compositions and arrangements, he draws inspiration from his intimate knowledge of traditional Russian folk music and folk songs.
Interpreting works of a specific composer in a specific style requires an understanding of the historical cultural/stylistic and social aspects/influences, considering music an expressive art. This is often called the study of performance practice, with attempts at historically informed performance (sometimes abbreviated HIP).