The third study in A major from Matteo Carcassi's 25 Melodious Studies for Guitar. Although it is in major key, it sounds melancholic, and its chord progression is beautiful.
Op9 "Variations over a theme from the Magic Flute" by Fernando Sor. This variation is really hard, with this you can improve your slur technique and your damping technique.
The second study in A minor from Matteo Carcassi's 25 Melodious Studies for Guitar. The main purpose of this study is to develop the fingers of the right hand.
Here is the first study from Matteo Carcassi's 25 Melodious Studies for Guitar. With this study, you can develop right hand alternate picking, smooth left hand shifting, left hand finger independence for counterpoint and right hand arpeggio.
Here is another Study by Fernando Sor (1778-1839), this is an arpeggio study. While the left hand is pretty simple, the chord progression at the end is interesting, and it provides an excellent right hand workout.
Among the best left hand exercises. I usually use this for warm up, playing slowly. It will provide finger independence needed for playing counterpoint music on the guitar.