One of my favourite books for new knitters is Fearless Knitting Workbook by Jennifer Seiffert. I love this book because it has small projects of increasing difficulty with clear instructions. You can make a minimal investment in some cotton yarn, or even hemp, and turn each of these projects into a dishcloth. You learn techniques from knits and purls, to following a chart, to basic lace. I think that this book is a great investment for any knitter!
Of the books on my shelf, I find myself reaching for two books more often than any other. They are both written by the lovely Melissa Morgan-Oakes I am not a sock knitter so when I do knit socks it is important to me that they knit up quickly and efficiently. With these books you will learn to knit a pair of socks at the same time using magic look on a 100cm circular needle. The picture tutorial is so clear and the patterns in the book are beautiful. There's even a section at the back that tells you average foot length of different size feet for those knitworthy people in your life.
If you're at all interested in designing your own accessories I recommend Stephanie Pearl McFee's book, Knitting Rules. Although it's not detailed math equations for everything it does go into nice descriptions on how items like shawls, hats and socks are constructed. Her writing is very funny and she'll even give you some tips along the way on how to trick people that you're knitting them hand-wear by measuring their hands when in reality you'll be knitting them head-ware and foot-ware! Very clever book.
Finally, every knitting library needs a stitch dictionary or stitchonary. I have a few in my library and the two I visit often when designing my knitting are 400 Knit Stitches and Up, Down, All-Around Stitch Dictionary. Traditionally, stitch dictionaries have been written for items worked flat and a little brain power is necessary when adapting these stitch patterns for in the round. 400 Knit Stitches is like this whereas Up, Down All-Around has instructions for flat, in the round, from the top of a piece and from the bottom of a piece but less options. Both very good books.