Are you looking for a single book that concisely summarizes and derives all of the essential physics that a physicist needs to know? Such a book would not be just a list of formulas but would give enough of the derivation of the results that it could be understood by a physics graduate student or by an engineer or scientist with some physics training, or by an older physicist (like myself) seeking to brush up in some area. (There is also a place for physics formularies and encyclopedic collections, but here I'm interested in concise derivations of key results.)
The problem with finding such a perfect book is that physics is fundamentally hard. It is hard to derive in a single short book all of the interesting things that physicists have learned over the past couple of centuries and that usually require taking many courses and studying many textbooks to learn. Furthermore, no one book is at the right level for all physicists or graduate students, as we all have differences in what we have previously learned and differences in what we need to learn next.
Nevertheless, there are some books that make valiant attempts at this worthwhile goal of providing concise summaries of the key theories of physics. Two books that look to me to like they do a fairly good job in this attempt, though I haven't fully read either of them, are:
"Errata (and Suggestions) for The Six Core Theories of Modern Physics, by Charles F. Stevens." Errata by G.W. Hammett (2006).
One of the things that I like about Steven's Six Core Theories is that it is a very slim volume and it doesn't try to be encyclopedic like many physics textbooks. It instead focuses on explaining the logic behind these six core theories (Classical Mechanics, Electricity and Magnetism, Quantum Mechanics, Statistical Physics, Special Relativity, Quantum Field Theory, and an intro chapter on Mathematical Tools) and gives brief derivations that a serious physics student can follow. (Stevens is at the Salk Institute and did his Ph.D. many years ago in biophysics. He is a member of the National Academy of Sciences.)
Poole's book The Physics Handbook is somewhat broader, and thus the derivations are briefer. I think I found some mistakes in it as well (such as in a section regarding the effects of rotational degrees of freedom on ideal gas laws), but overall I found the sections I read quite helpful. One of the goals of this book is to help graduate students seeking to pull together their physics understanding. As he states in the preface:
"The first draft of the manuscript was assembled from notes I had accumulated during twenty years of teaching a qualifying examination preparation course...."
Other books in this genre include:
Princeton Guide to Advanced Physics, by Alan C. Tribble (Princeton University Press, 1996). Closer to Poole's book above, it has a large compendium of equations from many fields of physics.
Theoretical Astrophysics, Volume I: Astrophysical Processes, by T. Padmanabhan (Cambridge University Press, 2000). It has one chapter reviews of classical mechanics, special relativity, E&M, and statistical mechanics.
Galactic Dynamics, by James Binney and Scott Tremaine (Princeton University Press, 1987), has appendices devoted to summarizing Mathematical Background, Mechanics, Fluid Mechanics, and Cosmology.
Fundamentals of Plasma Physics by James D. Callen (a draft online textbook), has appendices with a few pages of summaries of Classical Mechanics, Electrodynamics, Statistical Mechanics, Fluid Mechanics, basic quantum effects, complex analysis, and other math tools.
Add more here?? more on complex analysis, plasma physics, quantum??
Useful links:
John Baez's "How to Learn Math and Physics".
MIT Graduate Women in Physics General Exam Guidelines lists some good physics books.
To really learn physics, it is essential to gain practice working through problems. ("But be ye doers of the word, and not hearers only, deceiving your own selves", as the Bible says.) This is particularly important for physics graduate students who face the challenge of passing qualifying exams (divided into the prelims and general exams at Princeton). For this, practice with actual exam questions is invaluable. Most physics departments distribute collections of exam questions from recent years for students to practice with, and some of these have been published in books:
Princeton Problems in Physics with Solutions, by Newbury, Ruhl, Staggs, et al. (1991).
This is based on actual Princeton University Physics Prelims (which cover the four topics of Classical Mechanics, E&M, Quantum Mechanics, and Statistical Mechanics), and physics General Exam problems (which also include general relativity and quantum field theory). A somewhat more recent collection of graduate physics exam problems from various universities is:
A Guide to Physics Problems: Part 1 (1994), Part 2 (1997) by Max Dresden (Foreword), Sidney B. Cahn, Gerald D. Mahan, Boris E. Nadgorny
Studying physics is hard, but it can also be fun as you begin to understand things that had been mysteries to you... Good luck.