The most common glues are Cyanoacrylate ("CA glue", "super glue") and epoxy. They work on everything.
People I know use an adhesive called E6000 with plastics, with good results, but I have yet to try it myself: it is easiest to get on eBay.
If you are doing much work with plastics, you sometimes want to use an adhesive with solvents in them - that melt the plastic and then evaporate, allowing the meld to cure. This is called "plastic welding".
These glues are often found in shops that sell plastic model kits and also in building supply stores that sell plastic pipes.
However ... PBT is quite resilient to most solvents. I believe that
MEK could dissolve PBT but it is not as common in plastic adhesives as other solvents are.