  This paper gives a concise introduction into the basic theory of
{\omega}-automata (as of March 2014). The starting point are the different
types of recurrence conditions, modes of operation (deterministic,
nondeterministic, alternating automata), and directions (forward or backward
automata). The main focus is on fundamental automata constructions, for
instance, for boolean operations, determinization, disambiguation, and removing
alternation. It also covers some algebraic aspects such as congruences for
{\omega}-automata (and {\omega}-languages), basic structure theory (loops), and
applications in mathematical logic. This paper may eventually become a chapter
in a handbook of automata theory.
