Famously, a problem which stood for many years concerning Banach spaces was whether or not every one admitted a Schauder basis. This was discussed by many mathematicians, including Grothendieck! Finally Per Enflo published a paper in the 1970s giving an explicit example of a space without such a basis and indeed solving a number of other problems simultaneously (the space has an operator on it with no nontrivial proper invariant subspace etc.).
Numerous places online and my lecture course reference this fact but I can't seem to find any exposition of it. It's been something like 50 years since this example was found: surely someone has written a (potentially very long) article describing this space's construction and its properties? Is there such a text?
Preferably, any reference given would focus on this space and would be self-contained bar assuming basics in functional analysis (Hahn-Banach, Open Mapping theorem etc.) which you might learn in a first course. If this is not possible, a book with a chapter or two on this topic would also be acceptable.