Tim McCreight's The Complete Metalsmith.

Now in its fourth or fifth edition, it has split into three incarnations: the student book, the pro book, and the pro-plus book. The difference between them being that the student edition is a smaller toolbox friendly size, and contains an edited subset of the pages, while the Pro and Pro+ editions are larger and contain everything. The Pro+ has a CD with the whole book as printable PDF's. The PDF's are useful for me for printing things for class, but otherwise, I'd just get the pro edition, and save the money. The various editions of this book have been the texbook since I was in school. Every technique clearly illustrated with step-by-step drawings, and a vast range of techniques. There's a reason this has been the standard textbook for 20+ years. This should definitely be your first book.

Erhard Brepohl's Theory and Practice of Goldsmithing.

Originally published in East Germany in the '60s, it was one of the only East German books to make money in the West. It was that good. The irony of a book on jewelry making coming out of a communist country was not to be passed up, so the original edition (in German) has a truly hysterical chapter about how jewelry doesn't fit in with the idea of the worker's paradise. (The bits of it that I could read with what's left of my childhood German looked funny, at any rate.)
It should tell you something that I saw a copy of this when I was going to school in London, and went out and bought a copy in German; a language I could barely still speak, and couldn't really read, just to puzzle through the captions. There is information in here that isn't in any other book, anywhere.
Fortunately for you, Charles Lewton-Brain and Tim McCreight have labored mightily, and produced an English translation since that point. It should also tell you something that the next words out of my mouth after Charles told me that he was working on the translation were "Brepohl in English??! Who do I make out the check to, and when can I have it?" The translation is based on the 'revised' edition that Brepohl put out after the wall came down, and he could dispense with all the silliness that the East German authorities made him include. (The 'jewelry is bad' chapter, for example, is gone, much to the regret of comedians everywhere.)

Being a reasonably faithful translation of a German technical book, it's drier than dust. He starts with the electron, and proceeds from there. On the other hand, by the time you get to anything you'd recognize as metalsmithing, you know exactly why the metal behaves as it does, and what's going on at the most detailed level. This is not an easy read, but the reward of knowledge is absolutely worth the price of admission. My highest possible recommendation. The only reason I don't recommend it more highly than McCreight's metalsmith is that it is not a beginner's book. It is a book that any serious metalsmith should own however.

Oppi Untracht's Jewelry Concepts and Technology

Before Brepohl was available in English, this was the definitive 'bible' for technical information. It's still one of the very best of the big technical books. It covers a wider range of techniques in detail, and isn't as Germanically fanatical in its detail as Brepohl. It's a much more readable book. If the notion of trinary alloy charts, and valence shells doesn't sound like your idea of metalsmithing, this is your book. It's just as accurate, and nearly as detailed, without the overhead of needing to brush up on your college chemistry. Highest recommendation.

Oppi Untracht's Metal Techniques for Craftsmen

This was sort of the 'lite' version of Oppi's big book. (Concepts & Technology) It has much of the same technical information, without the cultural and ethnographic information that bulked out the big book. I've managed to survive all these years without a copy, but many people swear by it. I've had it in various studio libraries, and have always thought it to be a great book, but since I already have the big book, I didn't see the need to get the little one too. (Little being a relative thing: it's still about 1.5 inches thick and hardbound. The only thing that makes it 'little' is that the big book is nearly 3 inches thick.) It's also about half the price of the big book, so many students pick it up first. I can recommend it wholeheartedly.

Mark Grimwade's Introduction to Precious Metals (Second Edition)

Originally published in 1985, he’s just released (2009) a vastly updated and expanded second edition. For years, this was the only book in English that had any real metallurgical information about the precious metals, and it’s still the best. (The only other book that comes close is Brepohl, but Grimwade has the advantage of not being translated (albeit expertly) from technical German.) If you want to know whether or not to quench that 14kt white gold, and why nickel white does one thing while palladium white does another, this is the book to tell you. If you want to know why sterling gets ‘slushy’ before it melts, but fine silver doesn’t, the answer’s in here. If you’re planning on being a serious metalsmith, you need this one.

Thomas Glover's The Pocket Ref

You've heard the phrase "that's the oldest trick in the book"? This is that book.

A small, pocket sized volume containing 768 pages crammed with every formula, specification or other piece of oddball trivia you could concieve of, and many that you haven't yet. This isn't strictly jewelry related, but more aimed at the general engineering/machinist/'maker of things' crowd. Everything from all those high-school geometry formulae that you've forgotten, to first aid information, to strength and ratings of tool steel, to thread charts for metric, inch, (and even Witworth) threads. It even has meteorological charts. This book may raise your ubergeek status, and will definitely save your bacon at some point.

Megan Corwin's Chasing and Repoussé

Megan's long awaited book on chasing & repouseé is finally out, and it was well worth the wait. She goes into greater depth on many techniques than the other common books on the subject, and covers tool making and refining in vastly greater depth. She also covers a wider variety of chasing styles than the common texts. Chasing & Repuseé are sort of like chess: the basic rules can be learned in an afternoon, but mastery requires a lifetime of study. This 'simple yet complex' nature leads to a wide range of visual styles all generated by the same simple tools and techniques. She makes a point to cover both flat linework chasing, as well as fully 3-D and volumetric forming. Easily the best book on the market at the moment to cover these subjects.

Kevin Coates: A Hidden Alchemy. Goldsmithing, Jewels & Tablepieces

Kevin Coates is a British jeweller, who works in...pretty much anything he wants. Very figurative work, starting out in the early '70s with innovative use of titanium, largely for its colour. He also works extensively with baroque and handcarved stones, incorporating them into the figurative portions of the work. He's still one of my two favorite people for using titanium for his own purposes, rather than letting the titanium use him. Stunning stuff. I saw an exhibition of his work at Goldsmith's when I was a student in London. I've been a fan ever since. Imagine someone who does figurative work with outstanding craftsmanship. Imagine someone who makes pieces that pun...in Latin. He makes work that assumes that the viewer's well educated enough to either get the joke, or follow the references, and refuses to dumb down for those that don't get it.

Meanwhile, the book: 315 pages, hardbound, full colour throughout. It's not exactly a retrospective, but more of a collection of work, with critical evaluations by several authors. However the most important thing is the pictures. Full colour pictures of all of his pieces, up through 2007. Full page images of many of them, along with explanations and technical notes for some. You could (and I have) spend days just looking at the pictures.
I'm at a loss to describe the book itself without turning it into an explanation of Coates' work, and that's rather the point: his work is the point of the book. This is the first time all the work has been available in colour, all in one place, with explanations. If you're at all interested in seeing just how metaphorical and figurative jewellery can get, and still be jewellery, (as opposed to academic studies) you need to see this book. If you're interested in how to incorporate intelligent references into jewellery without turning it into a steaming pile of inscrutability, you need to see this.

I don't impress easily. Coates is one of two people who have made my jaw bounce off the floor.

Daniel Brush: Gold Without Boundaries

Daniel Brush is the other metalsmith who has made my jaw bounce. He’s very reclusive, and I’d never heard of him when I wandered into the Renwick one summer’s day. Several hours later after my friends dragged me bodily out of the exhibition, I knew I’d discovered a metalsmith’s metalsmith. As stunning as this book is, it pales in comparison to the real pieces. Go see them if you ever get the chance. Brush is a technical virtuoso, and seems to exult in pieces that are technically horrifying, but executed so cleanly that the uninitiated would never guess just exactly what a tour-de-force they really are. One of my favorite pieces has a several inch diameter dome of 22 karat gold. Granulated. Perfectly. According to legend, he had to sweep his shop for 7 months before he could get his head into the right place to fire that thing. The thing about fusion granulation is that you’re dancing along the ragged edge of melting the piece while you do it. There’s maybe a 20 degree window between not hot enough, and a puddle. With inches of 22 karat gold. I don’t even know where to begin, except to finish by saying that this is someone worthy of absolute respect.

Robert Pirsig's Zen & the Art of Motorcycle Maintenance

Really. Yes, the book's a refugee from the '70's, and no, it doesn't have anything to do with jewelry. In fact, to borrow a quote from the author, it doesn't have anything to do with zen, or even much to do with motorcycle maintenance.
It's about quality. It's about the urge to create things that have quality, and the kind of mind that has that urge. In that sense, it's absolutely about jewelry, because it's about craftsmanship. If you're the sort of person who wants to make something unique and beautiful, rather than buying mass produced drek, this book will speak to you. If you're reading this page, trust me, you need to read this book.

Margaret Livingstone's Vision & Art: the Biology of Seeing

This has nothing to do with jewelry. It's about how the brain and eye work together to see the world around us. If you've ever wondered how the Mona-Lisa's smile works, or why impressionist paintings seem to vibrate when you see them in person, but just lay there when you see them as posters, she explains it. The book is based on recent neurobiology and perceptual research, and is solidly grounded in real information, but it's written in a way that the average artist can understand and engage with it. This mostly has to do with painting and 2-D art, and how the brain perceives it, but it's wonderful info. Even for us 3-D artist/jeweler types, understanding how our viewers think about what they see can never be a bad thing.

Frank Wilson's The Hand: How its Use Shapes the Brain, Language, and Human Culture

This book has everything to do with jewelry. It's about how the hand and brain work together. It's about how the things we do with our hands at an early age actually change the physical development and structure of our brains; how the structures of the brain influence what we do with our hands, and how the two evolved together. The first time I read this, it was like a flashbulb exploding: it illuminated so much of what I'd noticed about the difference between how craftspeople use their hands, and think about making things, versus non craftspeople. Their brains are different. Really. Every craftsperson I've talked to who's read it has found it vastly informative. Just read it. Trust me. It's written in a very clear and jargon free style. Very easy to read.