Well done!
The piece reminds me of some Bach pieces for Solo Violin. Have you taken works by Bach as an example? It appears to be, but I like how you add a new, fresh touch to the music. You have nice melodies, but they can be developed more, as ilv said.
I agree with Luis; the score frightens me. I think Luis doesn't mean the notes, but the actual lay-out. You said the following in answer to him:
The difference regarding lay-out between Bach's Sonata and your Larghetto is huge. Not to be rude, but the Bach's score is clear and easily readable and yours is much harder to read:
Rests everywhere, not even merged (for instance. m. 1. two quarter rests can be merged into one half rest.).
When you look carefully at the other voices (not the first) of the Bach's Sonata you notice that the other voices except the first have some places where they don't sound, but there are no rests notated. I dare not to say if you may leave out the rests in your piece, but at you can merge the rests that can be merged.
Furthermore there are overlap issues:
For instance m.4. Very awkward, because quarter note on the fourth beat is overlapped by a quarter-rest.
You definitely have to take more care about the final stage, the lay-out, because this is what the performers see when they play your music. Make it as readable and understandale as possible for them.
More about the music itself, I think this is a nice introduction to a set of contrasting movements. Maybe you can consider to write a suite for it to stay with Bach.
Overall nice job.