  Logical relations (LR) have been around for many years, and today they are
used in many formal results. However, it can be difficult to LR beginners to
find a good place to start to learn. Papers often use highly specialized LRs
that use the latest advances of the technique which makes it impossible to make
a proper presentation within the page limit.
  This note is a good starting point for beginners that want to learn about
LRs. Almost no prerequisite knowledge is assumed, and the note starts from the
very basics. The note covers the following: LRs for proving normalization and
type safety of simply typed lambda calculus, relational substitutions for
reasoning about universal and existential types, step-indexing for reasoning
about recursive types, and worlds for reasoning about references.
