When was the tap invented?

There are many different meanings for 'Tap'. What kind are you talking about?

Try re-posting your question, but include what kind of tap you mean, OK?

Different taps:

Metal plate on a tap-dance shoe

Tap driven into a tree to extract syrup

Tap used to make threads in a hole

Tap used to dispense beer by being driven into the bung.

A (usually) unlawful connection to someone's telephone