You should understand the difference between a value conversion "cast"
like "(int) 3.0" that creates a new value, and a type conversion cast
that only re-interprets existing bits.

To understand the papers, you should know the term "currying":
https://en.wikipedia.org/wiki/Currying .

There is a typo in the 1982 paper, Algorithm W part (ii):  on the
second line, e2 and t2 should be e1 and t1.  "e2" and "t2" are correct
on the third line.

What is the distinction between
  \cal{E}[[e]]E
and
  A |- e : \sigma
?  Explain in 2-4 sentences.
(Read "\cal{E}[[e]]E" as as LaTeX code.  "\cal{E}" is the script letter E.
"[[ ]]" are double square brackets that are smashed together, in
"blackboard bold" style.)

What does "type safety" mean?  Why do we care?  How far do those
guarantees extend?