  These notes present a brief introduction to `naturalness' problems in
cosmology, and to the Cosmological Constant Problem in particular. The main
focus is the `old' cosmological constant problem, though the more recent
variants are also briefly discussed. Several notions of naturalness are
defined, including the closely related ideas of technical naturalness and `t
Hooft naturalness, and it is shown why these naturally arise when cosmology is
embedded within a framework --- effective field theories --- that efficiently
captures what is consistent with what is known about the physics of smaller
distances. Some care is taken to clarify conceptual issues, such as the
relevance or not of quadratic divergences, about which some confusion has
arisen over the years. A set of minimal criteria are formulated against which
proposed solutions to the problem can be judged, and a brief overview made of
the general limitations of most of the approaches. A somewhat more in-depth
discussion is provided of what I view as the most promising approach. These
notes are aimed at graduate students with a basic working knowledge of quantum
field theory and cosmology, but with no detailed knowledge of particle physics.
