The "logic" of the Enigma machine and the development of the Polish solution, in principle, are well described in David Kahn's "Seizing The Enigma". There may be better descriptions that have come out since, but I found this very clear and continue to recommend it. In addition to the nuts and bolts of the machine itself, Kahn describes the history from pre-war commercial tool to military tool, the creation of the reflector and additional rotors so that the 3 rotor tool could have both more transpositions and a larger mix of possible transpositions, and finally the addition of the 4th rotor position.
Crucially, he compares the security of different ways of using the machine, explaining why the German Navy's use of the same machine was harder for the British to break than the German Army or Air Force use. He describes the difficulties between the principle of the Poles' solution and the mechanics of an actual implementation, and provides a sketch of why Alan Turing's work was so important. He also points out how having a current German Navy code book, a present from the Soviets, allowed the British to realize what they were missing. The British made it their business to have the current Naval code book, meaning getting a new one every 6 months, for the rest of the war.
It was the confluence of all this work that allowed the comprehensive success of the effort to break Enigma. And, always, assisted by the over-confidence of the German authorities. Understanding how Enigma worked, including its logic and the logic of its use, shouldn't be separated from its complete failure in application.
"Seizing the enigma
the race to break the German U-boat codes, 1939-1943"
Published 1996 by Arrow Books in London .
Written in English.
Includes bibliographical references (p. -326) and index.
Dewey Decimal Class 940.5485, 940.548641
Library of Congress DS810.C88 K34 1996
The Physical Object
Pagination xii, 336 p.,  p. of plates :
Number of pages 336
Open Library OL24935024M
Internet Archive seizingenigmarac00kahn
ISBN 10 0099784114
ISBN 13 9780099784111