“What are the different types of contact lenses available for astigmatism?”

There are many toric contact lenses that can correct your astigmatism. These include Cooper Biofinity, Cooper My Day Toric, Acuvue Oasys for Astigmatism, Air Optix for Astigmatism, Precision 1-Day Dailies for Astigmatism, Alcon Total for Astigmatism, Bausch and Lomb Ultra for Astigmatism Cooper Proclear Toric, and Avaira Vitality Toric to name a few. These contact lenses are defined by the base curve which must fit your eye, the prescription, the thickness, the diameter, and the Dk value which is the oxygen transmissibility.
It is important that your eye doctor does a "fitting" which will allow you to be sure that you see well and that the lenses are comfortable and affordable. And you will be provided a "lesson" so that you know everything about your contact lenses including proper insertion and removal, how long to use them for, what solutions must be used to clean and to store the lenses, and when you need to return for follow-up care. Good luck and best wishes.