Is there surgery to build gum tissue back where the gums have receded?

Yes, there is a gum graft (root coverage) procedure that covers receded gums. Tissue is usually taken from the palate and grafted onto the receded area, and it is considered when 1) exposed roots are very sensitive, 2) the exposed area is notched and at risk of decay or wear, or 3) a receded gum line on the front teeth bothers you cosmetically. How much can be covered depends on the extent of the recession and the remaining gum tissue, so we first confirm whether it applies to you after an examination.