Hypnotism, as we know it today, can be traced back to the ancient world, though the term itself only dates back to 1842. In ancient India, Egypt, and Greece, hypnosis was used to cure disease through suggestion in "sleep houses," but the modern term identifies hypnosis as a different state than sleep.
The concept of hypnosis experienced its first boom around 1770, when Franz Mesmer began his famous studies into what he called "animal magnetism" and which we remember today as "mesmerism." In this theory, Mesmer indicated that there was a "magnetic fluid" that could be affected to cure various ailments. This "fluid" was later debunked, but it was noted that suggestion was the central cause of Mesmer's cures. This led to a number of people working in the direction of what would be later termed "hypnosis," such as Abbé Faria, who helped develop the concept of autosuggestion, and gave demonstrations of Mesmer's "animal magnetism" without using magnets.
Eventually, James Braid would develop these ideas in a different direction, coining the term "hypnosis" in 1842 (later trying to change the word to "monoideaism" and failing) and centering his own theories on the idea of inducing a hypnotic state by visual fixation, which led to many experiemnts in the use of hypnosis for medical purposes, including the use of hypnosis to replace anesthesia.
In the 1880's, hypnotism moved from the medical arena to areas of mental health. Hypnosis was used to cure hysteria and to recover repressed memories, and objections were raised by the Catholic Church, on the grounds that hypnotism could remove a persons's ability to reason, which is a sin if used for no just reason.
Since then, hypnotism has been used in psychoanalysis, leadership studies (the concept that leadership skills are partially group hypnosis and suggestion), and PTSD treatment. The concept is no longer identified with sleep of any sort, and we now have six levels of hypnosis (called the Arons Scale). Rapid induction (as opposed to relaxation progression) has also been recently developed.