Researchers at the NIH have conducted prior studies to establish synthetic human parathyroid hormone 1-34 (HPTH) as a treatment for hypoparathyroidism. Other studies have shown that PTH may improve calcium levels in blood and urine. The primary purpose of this research study is to evaluate the effects of synthetic human parathyroid hormone 1-34 (HPTH) replacement therapy on bone in adults and teenagers with hypoparathyroidism.