A major (or the key of A) is a major scale with a base note of A. Its key signature has three sharps.
relative minor is F-sharp minor. The key of A-major is the only key where a Neapolitan sixth chord on needs both a flat and a natural accidental.
There are not as many symphonies in A major as in
D major or G major, but more than other sharp keys. Beethoven's Symphony No. 7, Bruckner's Symphony No. 6 and Mendelssohn's Symphony No. 4 are almost all the symphonies in this key in the Romantic era. Mozart's Clarinet Concerto and Clarinet Quintet are both in A major. Mozart used clarinets in A major often. 
In chamber music, A major is used a lot.
Johannes Brahms, César Franck, and Gabriel Fauré wrote violin sonatas in A major. Peter Cropper said that A major "is the fullest sounding key for the violin.", when he was talking about Beethoven's Kreutzer Sonata. 
Christian Friedrich Daniel Schubart, A major is a key that is good for "declarations of innocent love, ... hope of seeing one's beloved again when parting; youthful cheerfulness and trust in God." 
Ascending and descending
When music for orchestra is in A major, the
timpani are normally set to A and E a fifth apart. In most other keys, they are set a fourth apart.
↑ Mark Anson-Cartwright, "Chromatic Features of E♭-Major Works of the Classical Period" Music Theory Spectrum 22 2 (2000): 178
↑ Peter Cropper "Beethoven's Violin Sonata in A major, Op.47 'Kreutzer': First Movement" The Strad March 2009, p. 64
↑ Rita Steblin: A History of Key Characteristics in the Eighteenth and Early Nineteenth Centuries (Rochester, University of Rochester Press: 1996) p. 123
Mozart: Clarinet Concerto, A Cambridge Music Handbook, Cambridge University Press, 1996.
Diatonic Scales and Keys
The table shows the number of sharps or flats in each scale. Minor scales are written in lower case.