Back in the day there was Feynman's Lectures on Computation. Hint: pdf can be found by searching
See also nLab
one should never forget Jacob Lurie's "Higher Topos Theory" which is 1000 pages just like that
Actually I recommend against readin it as it only covers 2 of the 4 topics you discuss (Topology and Logic). However it certainly has applications to the other two.
Feynman worked on this subject working on the Connection Machine supecomputer. 
So I gave up and continued reading. Then somewhere in the 4th or 5th Chapter he says something like: Oh I hope you had fun with the Firing Squad Problem, I still work on it from time to time and hope to come up with a solution myself one day.
Edit: Here is a link to the book, its enjoyable for experts and laymen alike.
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