Introduction
Classical (and some Romantic) music relied heavily on forms and structure. Sonatas, symphonies, concertos and string quartets were divided into 'movements'. Each movement followed specific formats or styles that were strictly defined. The most widely-used of these formats was 'sonata form'.

Usage
Sonata form was often used for first movements of Classic pieces. For this reason it is sometimes called first movement form but this is technically inaccurate as it was widely used for other movements, most often the fourth, as well. As most first movements used this format, the sonata form's 'task' was to set the tone for the rest of the piece. It always began and ended in the piece's tonic key (the key that appears in the title of the piece), though modulation could (and usually does) take place during the movement itself.

Elements
Sonata form consists of three (and sometimes four) sections.

  1. Exposition
    The first section of a sonata form always begins in the piece's original key. It contains one of the movement's main themes. The piece then modulates to a second key -- often the relative major or dominant key (though not always) -- and now contains a second theme (or a variation on the first theme -- some composers, including Haydn, repeated the first theme instead). All expositions are ended by a perfect cadence.

  2. Development
    A popular metaphor for the development section is that it's the exposition in a blender. The themes from the exposition are played again but are often mixed up and are played in a variety of different keys. The order is also most often mixed up. It generally also has a faster tempo and is often the center of 'tension' in the movement. The development does not end with a cadence; it instead leads directly into the recapitulation section.

  3. Recapitulation
    The final major section is in the original key and contains the themes from the exposition. Unlike the exposition, however, all themes are in the tonic key; movements using sonata form always end in the tonic key.

  4. Coda (optional)
    The coda section was not always used, but can be added to the end of the recapitulation to end the movement. The coda was most often a short cadence. Some composers had the coda lead into a second development section.

One of the main characteristics of sonata form was its tempo. Movements written in sonata form were almost always fast and serious. They contained easily singable or memorable melodies.

The exposition was often played twice, and in the early classical era the development and recapitulation were often repeated. Some sources indicate that this practice was phased out around 1780.

Variations
Sonata form was also often called sonata-allegro form. This was because the movements in sonata form were, as aforementioned, played allegro and were more 'serious' in nature. Sonata form is also sometimes called compound binary form.

The sonata form used in concertos is different from the sonata form used in string quartets, symphonies and sonatas. As in several other sonata forms, the exposition is played twice however it is not simply repeated. The full orchestra plays the main themes first entirely in the tonic key and then plays the accompaniment as the solo instrument plays the themes -- but the solo instrument modulates before the second theme.

The Romantic Era
Convention and structure was a key element of the Classic era, however some early Romantic music made use of the classical forms. Many Romantic composers used sonata form for each movement of their pieces, modifying conventional structure. Less emphasis was placed on use of the dominant keys; Romantic composers modulated their pieces to the mediant keys and relied more on the use of Terzverwandschafts or third relations (thanks, tdent!). The use of repetition in Classical sonata form also decreased during the Romantic era.

The Modern Era
Many composers during the Modern era placed emphasis on atonality. Variations on sonata form were used by composers such as Schoenberg, Sibelius and Prokofiev, though 'sonata form' as Classical composers knew it was not used as widely. Wikipedia estimates that "by the 1930s, 'sonata form' was merely a rhetorical term for a movement which stated themes, took them apart and put them back together again." Several other composers were influenced by the Classical structures but used different tonal systems.


Resource:
Yudkin, Jeremy. Understanding Music: Third Edition. Prentice Hall: Saddle River, NJ. 2002.
Sonata form http://www.fact-index.com/s/so/sonata_form.html 15 June 2004
Sonata form http://en.wikipedia.org/wiki/Sonata_form 16 June 2004