I’m fairly new to grasping this concept so take it easy on me. In the following piece which I assume is 4/4 the sum of the notes simply do not add up. Lots of 32nd notes and some quarter notes equalling far more per bar than there should be. What am I missing I’m this time signature?
The smaller notes are grace notes. They don't count for the time signature. Traditionally there would be only one or a few per "main" note. Here, Paganini is basically saying to play these figures ornamentally and out of time.
This is especially underlined by the fact that there is no time signature and indeed there are no bar lines. There are no measures; there is no meter. Play the notes freely.
Since there is no time signature, it's no good trying to guess one!
The one beat notes (crotchets, 1/4 notes), are the target notes the violinist will aim for, and play for a little longer than the flurry of other notes, which show how much of a virtuoso s/he is. Those notes are called grace notes, or ornaments, which a player like Paganini would play often, showing his prowess as a violinist. The notes themselves have little or no note timing value on their own, and are always written with smaller heads and stems to show this. Because there's no time signature, or even bar lines, there's going to be no 'pulse' running through that part of the Caprice.