TOPIC: Complex dynamics
USEFUL COURSES: Complex dynamics (obviously), Compex analysis, differentiation, analysis I/II , Metric spaces, Topology,
LEVEL: Moderate to high (proofs move up to 3 logical steps at a time)

There have been many things, over the past years, that have contributed to my love of mathematics; articles I have read, eyes struggling to stay open, each cone of my retina straining as I scrabble fruitlessly to understand cohomology on wikipedia, talks I have attended, and that irresistible enthusiasm of a committed mathematician in full flow. None have captured my imagination, appeased my sense of rigour or exposited that indefinable mixture of logic and inspiration that makes our subject so unparalleled so well as Milnor does in this book.

Milnor, whom I have heard described as the "enabler" to the John Nash of beautiful mind fame (at university, I am told, he is said to have taken great pleasure in enthusing the young mathematician into a frenzy), is a highly influential figure in many areas of mathematics (he discovered the existence of exotic manifolds, look em up, they're pretty hot!), and his text books are core texts for any course advanced enough to cover the material. In short: he is a bit of a legend.

The book, any mathematician of suitably high stature will tell you, goes "right from the ground up": a cursory reading of page two (where the uniformization theorem is unceremoniously thrown at you like a wet towel) will convince anyone with a brain that this is palpably b**locks. If you are attempting this book before the end of your third year, expect to struggle.

But your struggle will not be in vain if you do, over 273 pages Milnor introduces, with pitch perfect prose and a wonderful instinct for motivating examples, a theory that is as beautiful as it is deep. One to buy if you like your maths with pretty pictures.