
Mozart’s Symphony in G Minor, No. 40 (K550) was completed on July 25, 1788 in Vienna. Mozart has 626 pieces cataloged in total, and Mozart died on December 5, 1791, so Symphony No. 40 was composed near the end of Mozart’s life. Mozart's music falls into the Classical Period.
The beginning: Mozart was born in 1756. W.A. Mozart mastered his first piece before his fifth birthday. His father, Leopold Mozart jotted down in a journal that it took less than 30 minutes for Mozart to learn it. Leopold had immediate aims of continuing the musical education of W.A. Mozart, and his older sister, Anna Marie Mozart, who he took on their first tour to Munich in 1762. From the earliest stages, W.A. Mozart was celebrated as a prodigy of music.
Around the time of the composition: One of Mozart’s most famous compositions, Eine kleine Nachtmusik (K. 525) was composed in 1787, just one year before. Another of Mozart’s famous compositions, Don Giovanni (K. 527) premiered in the same year as Symphony No. 40, which ran for 15 performances at the National Court Theater. In the world during this time, the United States Constitution was being ratified.
About the composition: The form of the fourth movement of Symphony No. 40, and one of the most significant forms in the history of music, is the Sonata form. Starting in the late Baroque period, Sonata form has been widely used by composers and appreciated by theorists for now, hundreds of years. Some composers that frequently used Sonata form are Carl Philipp Emanuel Bach, Franz Joseph Haydn, and Ludwig van Beethoven.
Sonata form usually consists of an introduction, exposition, development, recapitulation, and coda.
The exposition introduces the main theme, transitions to a closely related key, introduces a secondary theme, and closes in a codetta, or short closing music, ending in a perfect authentic cadence in the new key, as to set up the development section.
First theme: (click on any picture to enlarge)

Second theme:

The development section contains sections of the first and second theme, altering them by modulating through new key regions, introducing or modifying motives, and occasionally juxtaposing, or melding themes together, creating a section of interesting and less stable rhythm and tonality, returning or ‘retransitioning’ to the original key of the piece, setting up for the recapitulation.
Developing the first theme at the beginning of the development:

The most beautiful feature of this famous work, is that the development section movies through three key regions and then comes a rapid spurt of fifteen keys and key regions (including borrowed keys and remote keys) over the course of 50 measures (m.151-201) before finally cadencing in the home key, g minor.
The recapitulation ‘recaps’ or restates the first theme, and transitions to the secondary theme, now in the ‘home’ key rather than a closely related key regaining stability to the piece, and thus setting the piece up for a closing.
Second Theme 'recapped' in the home key:

Although Symphony No.40 does not, a sonata can optionally end in a coda, which is an extension of the piece, usually to elaborate on past themes and motives, occasionally introducing new thematic material, called terminal development, and cadences in the original key of the piece.
Symphony No. 40 is written in G Minor, which according to studies of key meanings, is associated with seriousness and magnificence, combined with spirited loveliness, which you may listen for in the beautiful harmonies and textures of this piece.
Lastly, as you listen, you may use these guidelines to follow the form:
Exposition:
m.1 - Exposition begins in g minor(i = tonic), primary theme is introudced in a repeated period binary design.
m.32 - begin transition to secondary theme
m.70 - Secondary theme begins in Bb Major, (relative-major key(III) to home key, g minor(i))
m. 101 - the exposition comes to a close, cadencing in Bb Major in m. 124.
Development:
m.125 - Development begins developing the primary theme, then movies through 18 different keys and key regions before landing on tonic.
m.206 - Recapitulation begins, introducing the Primary theme, transition, and secondary theme in the home key, creating stability through the end of the piece.
Further research can be done here:
Boerner, Steve. "Biography." The Mozart Project. Web. 22 Jan. 2010.
Boerner, Steve. "Symphonies, Symphony Movements." The Mozart Project. Web. 22 Jan. 2010.
"A little history of the Sonata." Music history and timeline at Classical Works. Web. 22 Jan. 2010.
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