Quantum Theory: A Very Short Introduction | 
pickThe author takes a historical approach showing what problems with a Newtonian-based view quantum theory was reacting to and then how it has developed over the years. The easiest parts of the maths involved are relegated to an appendix, although the author stresses that it's impossible to fully understand the theory without the maths. Even in this stripped down form I was struggling but I think I did get glimmers of understanding here and there.
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