This Life of Fred: Metamathematics covers:
The subfields of math. 
Turing machines definition. 
Adding, subtracting, recognizing more than two symbols. 
The impossibility of locating all the non-blank symbols on an input tape. 
Turing machines with two tracks.  With two tapes. 
Unary notation. 
The universal computer. 
Turing machines on an infinite checkerboard instead of a tape. 
The halting problem. 
Dealing with negative numbers, copying a number, multiplying, exponentiation, projection and constant functions, determining if x > y. 
Doing logic computations. 
Doing geometry. 
True vs. provable. 
Gödel's First and Second Incompleteness Theorems. 
Computable functions defined. 
The Church-Turing thesis. 
Primitive recursive functions. 
General recursive functions. 
The Ackermann function. 
Self-replicating machines. 
P and NP functions.