Keith Devlin wrote one of my favourite maths books, so I was interested to see how he approached this subject. The Millennium problems are seven problems with a million dollar prize offered by the Clay Foundation. The level of difficulty in explaining them... varies significantly.
The early chapters deal with e.g. The Riemann hypothesis and P = NP, and it ends up with the Hodge conjecture. It's the usual kind of pop maths start-at-GCSE-level explanation. So, you'll be reintroduced to complex numbers yet again. By the time you get to the Hodge conjecture, which is genuinely difficult to explain, they've basically given up.
So, I'm at a bit of a loss with the book. It was effective at explaining easy things I understood, and not effective at explaining the things I didn't. After "Mathematics: The New Golden Age", it was a bit of a disappointment. Ah well.