An introduction to WKB analysis

The exact WKB analysis is a very effective method
in studying both linear and non-linear differential
equations which contain a large parameter in an appropriate
way. This talk consists of two parts.
In the first part, we will study the exact WKB analysis
introduced by Aoki-Kawai-Takei. In the second part,
we will discuss the construction of instanton-type
formal solutions of Painlevé hierarchy which play an
important role in description of the connection problems
of solutions.