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I don't understand how the first measure only has one quarter note and how the third one has three quarter notes and a half note, both measures don't seem to add up to 4 quarter notes like the time signature.

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The first measure is called a pickup measure. The music stars on the fourth beat, so the music would start with rests. Sometimes people will put the rests in, other times (as here) they will leave them out. This is also known as an 'anacrusis'.

The quarter notes in the third bar are 'triplets' (three notes in the space of two) recognizable from the '3' with the bracket above them. Triplet are one type of 'tuplet'. A tuplet is:

any rhythm that involves dividing the beat into a different number of equal subdivisions from that usually permitted by the time-signature (e.g., triplets, duplets, etc.)
[Carl Humphries, The Piano Handbook, 2002]

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    Probably worth noting that when a piece starts on a pickup, the "borrowed" time is taken out of the end. OP will undoubtedly observe that the last measure of this piece is in fact 3 beats long. – chrylis -cautiouslyoptimistic- Jun 13 at 12:41
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    @chrylis-cautiouslyoptimistic- That convention is rarely followed nowadays for anything except dance or folk music. – PiedPiper Jun 13 at 13:25
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    Interesting. I personally do not recall seeing a case where it wasn't. (Primarily choral and orchestral.) – chrylis -cautiouslyoptimistic- Jun 14 at 2:35
  • @chrylis-cautiouslyoptimistic- Take the first movement of Mahler's Symphony no.5 as an example. – PiedPiper Jun 14 at 9:01
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welcome to the community.

The G7 bit is not a measure but the end bit of a measure. This is called anacrusis. So the first measure is the CΔ one.

As for the measure with the 3 quarter notes, the "3" number indicates that the duration of those notes is shorter so that the available duration, that of 2 quarter notes, is shared by the 3 notes enclosed. That is called a triplet.

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