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.
There are also older, and very different topological models for typed lambda calculi (see e.g. http://www.cs.bham.ac.uk/~mhe/papers/entcs87.pdf). These motivate things like Escardo's "seemingly impossible functional programs" (http://math.andrej.com/2007/09/28/seemingly-impossible-funct...) and, along different lines, Abstract Stone Duality (http://www.paultaylor.eu/ASD/).
> 50 pages of pure cake, beautifully and informally written. The book is 1000 pages long. There is some new cake there, but not 20 times as much.