Lithium, normally in the form of lithium carbonate (Li₂CO₃) is widely recognised as the 'gold standard' prescribed drug for treating bipolar disorder, depression and mania.

In widespread use since the early 1970s, lithium carbonate was the first FDA approved drug for 'mood control'.

However, despite more than forty years of intense research, and millions of treated patients - "The precise mechanism of action of Li⁺ as a mood-stabilizing agent is currently unknown." Source : Wikipedia

In 1996 it was found that lithium inhibits GSK-3, a multi-tasking serine/threonine kinase enzyme which regulates several critical cellular functions. It's not known however, how this inhibition affects mood. (ref.)

Further, for reasons that are also unknown, therapeutic lithium has little or no effect on some individuals :

Lithium is generally regarded as the first-line agent for the management of BP, although it does not work for everyone. For instance, Geddes and colleagues performed a meta-analysis of five randomized controlled trials comparing prophylactic lithium therapy with placebo in BP and found that lithium is more effective than placebo in preventing recurrence of illness, with 60% in the lithium group remaining well over 1–2 years compared with 40% in the placebo group."

Source : External Predictors of Lithium Response in Bipolar Disorder Therapeutic Advances in Chronic Diseases, 2(3): 209–226

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Lamotrigine is used as an anticonvulsant and mood stabilizer. Currently prescribed in cases of epilepsy, Lennox–Gastaut syndrome and bipolar disorder. Its active biochemical pathways are not known. more info at Wikipedia

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The use of Ketamine to treat Major Depressive Disorder was formally investigated in a 2006 report for JAMA Psychiatry. A team based at the US National Institute of Mental Health (NIMH) in Bethesda, Maryland, found that :

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Current estimates are that severe depression affects around 2% of the global population at any given time, currently more than 150 million. The majority of cases don't appear to have an obvious personal and/or societal cause.