The document discusses various methods for dyeing polyester fibers, including: 1) Batch dyeing without carriers involves dyeing at a boil without additives to help penetration. 2) Carrier dyeing uses compounds to swell the fibers and allow deeper dye penetration. 3) High temperature, high pressure (HTHP) dyeing penetrates dye rapidly at over 120°C without carriers. 4) Continuous thermosol dyeing involves padding, drying, and fixing dye within fibers at 190-220°C.