In "Lecture Notes on Cryptography" what does "PTM" mean?
As pointed out by hakoja in the comments:


  It means Probabilistic Turing Machine, see Section B.2.1.


where the following is written (emphasis mine, this is the full section B.2.1):


  Let $M$ denote a probabilistic Turing machine (PTM). $M(x)$ will denote a
  probability space of the outcome of $M$ during its run on $x$. The
  statement $z\in M(x)$ indicates that $z$ was output by $M$ when running on
  input $x$. $\Pr[M(x) = z]$ is the probability of $z$ being the output of $M$ on
  input $x$ (where the probability is taken over the possible internal
  coin tosses made by $M$ during its execution). $M(x; y)$ will denote the
  outcome of $M$ on input $x$ when internal coin tosses are $y$.