As of May 21st, 2012, the purpose of this study is to test the antidepressant effect of ketamine when given repeatedly over a period of 1 week, as well as the use of Lithium as a relapse-prevention strategy for patients with treatment-resistant depression (TRD) who respond to an initial series of ketamine infusions. Ketamine is a Food and Drug Administration approved anesthetic (a drug used to produce loss of consciousness before and during surgery). Ketamine is not approved for the treatment of major depressive disorder and is considered experimental in this study.