This piece was written by Matteo Carcassi (1792-1853) and is the 7th from his 25 Studies for Guitar, op. 60. It is currently an ABRSM grade 4 set exam piece.
The piece is primarily in the key of A minor. The G#s (e.g. bars 2, 4 and 5) represent the raised leading note from the A harmonic minor scale. The second section (bar 9 onwards) starts in the relative major key, C major, and makes its way back to A minor by the end of the piece.
Right Hand Fingering
This is an arpeggio study, and is a gentle preparation for learning how to play the tremelo on guitar, the technique used in pieces such as Tarrega's famous Recuerdos de la Alhambra.
In bars 1, 5, 9, 13-15, 21, 25 and 26 we have groups of four semiquavers with the first note note played by the thumb (stems down) followed by the same higher note played three times by the fingers. The right hand fingering for each four note group in these bars is p a m i, the fingering used for a tremelo.
For most of the remainder of the piece we still have groups of four semiquavers where the thumb plays the first note. But because the following 3 higher notes now vary rather than repeat the same note three times, the suggested right hand fingering is:
Left Hand Fingering
p i a i where the high notes are not on adjacent strings, (e.g. in the first half of bar 2), or
p i m i where the high notes are on adjacent strings (e.g. in the second half of bar 2)
The obvious left hand fingering for the first bar is to use the 2nd finger for the repeated high A. The bass notes are played open for A, 3rd finger for C, 4th finger for F and 1st finger for E.
Bar 2 is actually quite awkward for the left hand to play smoothly. Here's the obvious fingering for this bar:
Carcassi Study, bar 2
Try this and you'll find you have to make a tricky jump with the second finger from the 8th to the 9th semiquaver (A to low B) that can break the flow of the piece, especially at faster speeds.
If you have a good left hand technique you might want to consider using this combination of weaker fingers, as it removes the awkward left hand jump:
Carcassi Study, bar 2, alternative fingering
Also if you use your third rather than second finger for the last two As in the bar (14th and 16th semiquavers) you'll find this sets you up nicely for bars 3 and 4.
I'll eventually be adding more study notes and an MP3 recording of this piece.