What they are:
Based on your question, you just want to know how to play them. While there are theoretical squabblers, just ignore the people go super into the theory.
It turns out there are two types of these small notes, and they get confused a lot.
- Appoggiatura (no strike-through)
- Acciaccatura (strike-through) Also known as "Grace notes"
What you're seeing in that piece are Appoggiaturas. They aren't grace notes. A grace note is actually a slang term for 'Acciaccatura' note which has a strike through. An appoggiatura does not have any strikethroughs. This might sound complex, but it's actually very simple, let's break it down with pictures!
- Small notation
- No strike-through
- Takes half value of connected note and played on beat (Longer value)
Acciaccaturas "Grace Notes":
- Small notation
- Has a strike-through
- Takes a VERY short value of the connected note (1/64th)
- Can be played both on or before the beat depending on composer/context
TL:DR No strike through = half value, LONGER | Strike through = very short
I hope this helps! If it answers your question, please mark as answered to keep up with maintenance. :)
These are called grace notes. Some good, already-written answers on this site can be found at Different types of grace notes and What do these grace notes mean, and how do I sing them?
These are called appoggiaturas, which are a type of grace note. These should be played on the beat of the note that they precede, and will (usually) be played for half the length of the main note.
Technically they are appoggiaturas, to be played on the beat taking half the length of the main note. A melodic suspension. The ones with a slashed tail are acciaccaturas, to be played as a short decoration to the main note.
But as the musical "grammar" of the example shown is so haphazard, I wouldn't be too sure the composer had the slightest idea what he wanted!