You can track animals or people if you are searching for or hunting them(To follow the course or trail of). You can trace a person or thing(To follow the course or trail of, past or present) . Monitor To test or sample, especially on a regular or ongoing basis To keep close watch over; supervise: You can monitor data looking for changes or trends as they happen(some people call this tracking, but it's use here is not suitable)

You could track, trace and monitor someone's movements. You can also trace someones movement back in time. You could also trace your ancestry. You can only monitor someones behavior and conversation. If you are a country or big internet company, you could track, trace and monitor somebody on the internet because we are talking about their movement over the internet. Again, if you were following what the person actually did on each site, you would be monitoring them, as opposed to both tracking and tracing.

I can break down the differences for you. When you track, you often plan to capture. You track with any means available. When you trace, you are following leads, one point to the next, forward in time or back in time. When you monitor, you do not trace back in time, you only look at the here and now - while possibly taking notes or records. It does not necessarily imply a plan to capture. Related and different.

Very excellent question.