I have recently (3 years ago) built a new home with a craw space. One day while I was under the house I noticed that under the master bedroom shower, on the septic tank side of the p trap, the plumber had installed a T about 1 foot from the P trap, and had duct tape over the top of the T, when I called him he said he must have missed it and had intended to install a studavent ( not sure of the spelling) What is this and shouldn't all my plumbing be vented through the roof?

The Studor vent is a particular brand of AAV (Automatic Air Admittance Valves) STUDOR® | IPS Corporation

They have very specific installation details. They are typically used inside cabinets where running a vent is impractical. They may be disallowed by code.