As a longtime homebrewer and former professional craft brewer, this is my favourite homebrewing book. The style is simple enough for beginners yet there is lots of information for more advanced brewers. Palmer guides you through brewing your first beer and also takes you to levels far beyond. If you become an avid homebrewer you will find yourself referring frequently to this book.
This book is considered by many to be the highest authority on the subject of home brewing. The author explains in painstaking detail every step of the process. You will learn how to brew at all three levels -- all extract, partial mash, and full grain. There is even a section (with diagrams) on how to make or modify the equipment you will need. This book in incredible resource, and one you will be referring to constantly as you grow as a home brewer.
As a new homebrewer, How to Brew gave me the confidence I needed to start brewing beer at home. This book is written for novice and veteran brewers alike. From simple, easy to understand instructions to start your first batch, right up to sophisticated mash/lauter tun flow vector diagrams.
All of the homebrewers I've talked to prefer this book. After reading it, I agree.