Classical music was a musical style that was popular in Europe in the 18th century. By convention, it begins in 1750, with the death of Johann Sebastian Bach, although "classical" music appeared earlier. The Classical era marked a move away from the intense emotionalism of the Baroque period towards a highly structured, stylistic manner, and was the flowering period of the sonata-allegro form (a three-part structure, with the first movement allegro, a slower second movement, and a faster--often allegro-- third movement). Later Classical-era symphonies often added a minuet-trio section as the third movement, and the faster third movement became the symphonic fourth movement. Popular composers include Haydn and Mozart.
Ludwig van Beethoven is sometimes considered to be a classical composer, but is a special case, as his early music was classical, and his later music romantic. In fact, his Pathetique sonata for piano is sometimes thought of as the piece that ushered in the romantic era.