The Western Music is divided to part according to time, i.e. they are divided into periods:
Baroque Classical Romantic Modern
Classical Music refers specifically to music composed between about 1750 and 1810 - a fairly brief period which includes the music of Haydn and Mozart, and the earlier compositions of Beethoven.
The Classical composers were mainly aware of the so-called "Classical-architecture" - grace and beauty of line (melody) and shape (the form or design used by a composer to build up his music), proportion and balance, moderation and control; polished and elegant in character with expressiveness and formal structure held in perfect balance. In particular, they strike a perfect balance in his music between expressiveness and formal structure. Most of the classical pieces are chordal, instead of contrapuntal in the Baroque Music. Classical music was lighter, clearer than Baroque, but they are less complicated.
The Classical Orchestra starts to grow a bit. No continuo again to fill the melodies and the woodwind family soon became a self-contained family, which consists of 2 flutes, 2 oboes, 2 clarinets and 2 bassoons.
The harpsichord was replaced by the piano. The piano is just a keyboard instrument, similar to harpsichord, but with loud and soft. So, by the end of the 18th century, the piano completely replaced the harpsichord.
Most of the classical music uses sonata form as its major form. The sonata form composes of three sections, namely the exposition, development and the recapitulation. The exposition introduces 2 themes, first in the original key and the other in its relative key, mainly dominant key. The development section develops the first and the second section within keys and may go through modulations. The recapitulation repeats the exposition, but with the two themes in the same key - the tonic key of the original key.
The sonata form was used on many occasions such as Symphony, Concerto, Sonata, etc.
Many classical composers wrote sonatas. Actually sonata was the name a Classical composer gave to a work in a few movements (usually three) for one or two instrument. The Symphony was in fact a sonata for orchestra, however, in four movements. The concerto features a solo instrument in competition with the orchestra. It has three movements and usually in "modified sonata form", which has double exposition, one for the solo and one for the orchestra. Towards the end of recapitulation, the soloists usually play a cadenza, which is a showy passage for the soloists to "show off" his/her brilliant technique.
Now listen to Mozart's Symphony No. 41 "Jupiter".