The Collaborative International Dictionary of English v.0.48:

Hypnotism \Hyp"no*tism\, n. [Gr. ? sleep: cf. F. hypnotisme.]
   1. A form of sleep or trance, in some respects resembling
      somnambulism, but brought on by artificial means, in which
      there is an unusual suspension of some powers, and an
      unusual activity of others, especially a heightened
      susceptibility to suggestion. It is induced by an action
      upon the nerves, through the medium of the senses, by
      causing the subject to gaze steadily at a very bright
      object held before the eyes, or on an oscillating object,
      or by pressure upon certain points of the surface of the
      body, usually accompanied by the speaking of the hypnotist
      in quiet soothing tones. Called also hypnosis.
      [1913 Webster +PJC]

   2. The science which deals with the induction and properties
      of the hypnotic state.
      [PJC]

The Collaborative International Dictionary of English v.0.48:

Mesmerism \Mes"mer*ism\, n. [From Mesmer, who first brought it
   into notice at Vienna, about 1775: cf. F. mesm['e]risme.]
   An earlier name for hypnosis or hypnotism, the art of
   inducing an extraordinary or abnormal state of the nervous
   system, in which the actor claims to control the actions, and
   communicate directly with the mind, of the recipient. It is
   believed to be a state between sleep and wakefulness, in
   which a person is more susceptible to suggestion than when
   awake. See Animal magnetism, under Magnetism.
   [1913 Webster]

WordNet (r) 3.0 (2006):

hypnotism
    n 1: the act of inducing hypnosis [syn: hypnotism,
         mesmerism, suggestion]

Moby Thesaurus II by Grady Ward, 1.0:

80 Moby Thesaurus words for "hypnotism":
   Arica movement, Erhard Seminars Training, New Consciousness,
   Pentothal interview, SAT, T-group, animal magnetism,
   assertiveness training, autosuggestion, behavior modification,
   behavior therapy, bioenergetics, biofeedback,
   confrontation therapy, conjoint therapy, consciousness raising,
   counseling, directive therapy, encounter therapy, est,
   family training, feminist therapy, gestalt therapy,
   group psychotherapy, group relations training,
   group sensitivity training, group therapy, humanistic therapy,
   hypnoanalysis, hypnology, hypnosis, hypnotherapy,
   hypnotic suggestion, marathon, marriage encounter, mesmerism,
   mesmerization, mind cure, narcoanalysis, narcohypnosis,
   narcosynthesis, narcotherapy, nondirective therapy,
   occupational therapy, od, odyl, odylic force, pastoral counseling,
   play therapy, posthypnotic suggestion, power of suggestion,
   primal therapy, prolonged narcosis, psychodrama,
   psychological counseling, psychosurgery, psychosynthesis,
   psychotherapeutics, psychotherapy, radical therapy,
   rational-emotive therapy, reality therapy, recreational therapy,
   regression therapy, release therapy, scream therapy, self-hypnosis,
   self-suggestion, sensitivity training, sensory awareness training,
   sleep treatment, suggestibility, suggestion therapy, suggestionism,
   supportive therapy, training group, transactional analysis,
   transcendental meditation, transpersonal therapy,
   vocational therapy