This is a partial list of the books we've found most useful over the years.
The Art of Electronics is the canonical introductory text to the subject, despite being more than twenty years old. As you might expect from that description, it is large, heavy, comprehensive, and can be terribly intimidating to newbies. Despite that, it is surprisingly well-written for a technical textbook and working through it will give you an excellent grounding in a variety of different facets of electronics.
This book is an great guide to applying electrical engineering concepts to real-world circuitry design. I find it an invaluable resource for turning theory into practice.
If Art of Electronics seems too heavy-weight for your liking, this relatively small and engaging tome from the patron saint of electronics hackers is an excellent alternative. Make sure to check out his other books as well.
This is another great book for turning theory into practice in electronics design. It has forty-five chapters covering different subjects, each one written by an expert on that subject.
This is my favorite Arduino book. I find the cookbook format really useful for getting straight to work and solving the problem(s) in front of me.
The essays in this book include many of the greats of analog circuit design of the past fifty years. I found the insight into the history of some of the most commonly used integrated circuits fascinating. And the tips and tricks for effective analog design will help you get better and faster results.
Radio & Wireless
If you're interested in radio communications, but not an electrical engineer, this is probably the most comprehensive reference on the market. It covers a broad range of radio topics in enough depth to get you started on building your own radios, antennas, and other gear.
The sections on radio regulations are more than good enough to give you the information you need to get a ham license. That license lets you use a much broader range of frequencies and at higher power than the general public is allowed. This is invaluable for projects that include radio control and telemetry.
Bluetooth Low Energy is a component of Bluetooth 4.0 positioned to compete with ZigBee and other low power networking protocols.
Robotics & Mechatronics
This is a fun little book about building super-cheap and remarkably capable robots written by the founder of Solarbotics. I first heard about BEAM robotics back in the mid-90s, on the old Principia Cybernetica website, and I was fascinated by the idea of building robots built around the impulses common to all living things. This book is a great practical introduction to the subject.
Maker community favorite Dustyn Roberts presents a great introduction to creating mechanical devices for a variety of applications. The book is focused on practical results with accessible fabrication techniques.
A classic introduction to robot building.
507 Mechanical Movements is a fascinating guide to many of the ways the engineers and mechanics developed for transferring, directing, and controlling motion before the development of modern electronic control systems. If you've ever been entranced by the entrails of a clock or an old wind-up toy, this book will entrance you all out of proportion to its diminutive size.
My first technical job of any kind was in a plasma physics lab, as an undergraduate research assistant. My professor suggested I pick up a copy of this book. It's a wonderful guide to building and operating all manner of unusual, precise, and just plain cool machinery. It has been near and dear to my heart ever since.
The first section is a brief but sound introduction to designing and making physical objects. It builds on this with sections on topics including vacuum systems, optics, electronics, working with glass, charged particle optics (make your own accelerator!), and a variety of other topics.
This is a broad guide to the various manufacturing processes available to industry, targeted at a professional engineering audience. However, it is written in an accessible style that makes it an invaluable reference work for anyone curious about the multitude of ways we humans have developed for cutting, mashing, bending, and otherwise forming the materials that make up the world around us.
David Lang became a professional maker after losing his corporate job. The skills and confidence he gained enabled him to co-found OpenROV, a company that manufactures open source underwater vehicle kits. This book chronicles his journey from unskilled bystander to successful maker-entrepreneur.
If you've ever watched the guys on Mythbusters pull a tiny little book out of their pocket to look up some obscure fact or guideline for what they're working on, this is the book they pull out. It's both invaluable and dirt cheap. The only downside is that the type is tiny. If your eyes are bad, you may want to pick up a magnifier or Desk Ref, which is much the same material at a more legible scale.
This is mathematics at its most concrete and applied. The book largely consists of useful geometrical and trigonometric formulas that are particularly useful for building physical objects.
Machinery's Handbook is the standard reference for the construction of mechanical things. It has comprehensive discussions of an enormous range of topics including fasteners, machining, mathematics, assembly and adjustment of moving parts, manufacturing processes, and many, many other things. It has been continuously in print, with frequent updates, for more than a century. However, in order to keep the book at a manageable size, the paper is so thin as to be translucent, which some people find distracting.