  Newton-Hooke space-times are the non-relativistic limit of (anti-)de Sitter
space-times. We investigate some peculiar facts about the Newton-Hooke
space-times, among which the "extraordinary Newton-Hooke quantum mechanics" and
the "anomalous Newton-Hooke space-times" are discussed in detail. Analysis on
the Lagrangian/action formalism is performed in the discussion of the
Newton-Hooke quantum mechanics, where the path integral point of view plays an
important role, and the physically measurable density of probability is
clarified.
