Wolfgang Amadeus Mozart is widely regarded as one of the greatest composers of all. Born in 1756 in Salzburg, he was the son of Leopold and Anna Maria Pertl Mozart. In his early years he and his sister Nannerl (also a gifted musician) were taught by their father and once the children's talents became clear the family travelled to courts all over Europe.
To begin with Mozart worked under the patronage system, employed from 1773 until 1781 by Prince-Archbishop Colloredo of Salzburg. During this time he took long trips away from Salzburg looking for work elsewhere. Eventually he was dismissed by the Archbishop (following attempts to resign which were not accepted) and moved to Vienna, where he worked independently until his death in 1791. As such he became one of the first composers to work independently rather than writing music to order, as most composers did at that time. For a time this was very successful but he had considerable financial difficulties in the last year or so of his life.
Mozart's importance cannot be underestimated. He wrote over 600 works and of course many of these are not great pieces of music (though they are very attractive to listen to). Amongst the works that are important you should look out for his Clarinet Quintet K581, the opera Le Nozze Di Figaro (The Marriage of Figaro), Eine Kleine Nachtmusik (K 525) and the Linz Symphony No. 36 in C Major, K 425. He is also best known for his String Quartets and Quintets, his operas (Cosi fan Tutte and Don Giovanni are two more you should look out for), his Piano Sonatas and his Piano Concerti.
Mozart's music has featured in a number of films. In Elvira Madigan the Piano Concerto in C K467 is used. Out of Africa features the music from the Clarinet Quintet K 525, and the film Amadeus also covered several different works including the opera The Magic Flute (Die Zauberflote).
There are a couple of things to be aware of when choosing a Mozart performance to listen to. Up until about the 1970s all recordings were performed on modern string instruments, with the singing style in the same way. However, the instruments of Mozart's time were not quite the same as they are today and in particular the piano was still in its infancy as far as construction is concerned. So since the 1980s an increasing number of performances have been played on period instruments, reconstructed in the style of the instruments of Mozart's time and there are now singers, choirs and music groups who can perform the music in this style. Both ways of performing the music are perfectly acceptable and what is important is whether or not you like the performance.