Amaj7 is built from A, C#, E and G#. A is the root, C# the major third, E the fifth and G# the major seventh. Said aloud, its notes are A, C sharp, E and G sharp.
String by string, low to high, it plays A, E, G#, C# and E. E appears twice in the main shape, and it is the chord's fifth. It runs from A on string 5 up to E on string 1.
The open strings add notes to Amaj7 too. String 5 gives A and string 1 gives E. String 6 is not played. Your hand covers two frets, from 1 to 2. There is one more position, starting at fret 5.
Change only string 3 in Amaj7 and you have A. Inside Amaj7 sits a complete C#m chord, made of C#, E and G#. Moving to E7, you keep one finger down.
Amaj7 belongs to four keys. In A major it is the I, in E major the IV and in C# minor the VI. The rest appear in the key list.