Reddit mentions of A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity

Friend asked for a similar list a while ago and I put this together. Would love to see people thoughts/feedback.

Very High Level Introductions:

• Mr. Tompkins in Paperback
  
  • A super fast read that spends less time looking at the "how" but focused instead on the ramifications and impacts. Covers both GR as well as QM but is very high level with both of them. Avoids getting into the details and explaining the why.
    
    
• Einstein's Relativity and the Quantum Revolution (Great Courses lecture)
  
  • This is a great intro to the field of non-classical physics. This walks through GR and QM in a very approachable fashion. More "nuts and bolts" than Mr. Tompkins but longer/more detailed at the same time.
    
    
    Deeper Pop-sci Dives (probably in this order):
    
    
• Quantum Theory: A Very Brief Introduction
  
  • Great introduction to QM. Doesn't really touch on QFT (which is a good thing at this point) and spends a great deal of time (compared to other texts) discussing the nature of QM interpretation and the challenges around that topic.
    
• The Lightness of Being: Mass, Ether, and the Unification of Forces
  
  • Now we're starting to get into the good stuff. QFT begins to come to the forefront. This book starts to dive into explaining some of the macro elements we see as explained by QM forces. A large part of the book is spent on symmetries and where a proton/nucleon's gluon binding mass comes from (a.k.a. ~95% of the mass we personally experience).
    
• The Higgs Boson and Beyond (Great Courses lecture)
  
  • Great lecture done by Sean Carroll around the time the Higgs boson's discovery was announced. It's a good combination of what role the Higgs plays in particle physics, why it's important and what's next. Also spends a little bit of time discussing how colliders like the LHC work.
    
• Mysteries of Modern Physics: Time (Great Courses lecture)
  
  • Not really heavy on QM at all, however I think it does best to do this lecture after having a bit of the physics under your belt first. The odd nature of time symmetry in the fundamental forces and what that means with regards to our understanding of time as we experience it is more impactful with the additional knowledge (but, like I said, not absolutely required).
    
• Deep Down Things: The Breathtaking Beauty of Particle Physics
  
  • This is not a mathematical approach like "A Most Incomprehensible Thing" are but it's subject matter is more advanced and the resulting math (at least) an order of magnitude harder (so it's a good thing it's skipped). This is a "high level deep dive" (whatever that means) into QFT though and so discussion of pure abstract math is a huge focus. Lie groups, spontaneous symmetry breaking, internal symmetry spaces etc. are covered.
    
• The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
  
  • This is your desert after working through everything above. Had to include something about string theory here. Not a technical book at all but best to be familiar with QM concepts before diving in.
    
    Blending the line between pop-sci and mathematical (these books are not meant to be read and put away but instead read, re-read and pondered):
    
    
• A Most Incomprehensible Thing: Intro to GR
  
  • Sorry, this is GR specific and nothing to do with QM directly. However I think it's a great book acting as an introduction. Definitely don't go audible/kindle. Get the hard copy. Lots of equations. Tensor calculus, Lorentz transforms, Einstein field equations, etc. While it isn't a rigorous textbook it is, at it's core, a mathematics based description not analogies. Falls apart at the end, after all, it can't be rigorous and accessible at the same time, but still well worth the read.
    
• The Theoretical Minimum: What You Need to Know to Start Doing Physics
  
  • Not QM at all. However it is a great introduction to using math as a tool for describing our reality and since it's using it to describe classical mechanics you get to employ all of your classical intuition that you've worked on your entire life. This means you can focus on the idea of using math as a descriptive tool and not as a tool to inform your intuition. Which then would lead us to...
    
• Quantum Mechanics: The Theoretical Minimum
  
  • Great introduction that uses math in a descriptive way AND to inform our intuition.
    
• The Road to Reality: A Complete Guide to the Laws of the Universe
  
  • Incredible book. I think the best way to describe this book is a massive guidebook. You probably won't be able to get through each of the topics based solely on the information presented in the book but the book gives you the tools and knowledge to ask the right questions (which, frankly, as anybody familiar with the topic knows, is actually the hardest part). You're going to be knocking your head against a brick wall plenty with this book. But that's ok, the feeling when the brick wall finally succumbs to your repeated headbutts makes it all worth while.

One book that is both inexpensive and generally well received is Peter Collier's A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity.

I think this book by Collier. should match up relatively^haha well with what you're looking for.

If you have a have a math background up to ODEs and PDEs, this book is great. https://www.amazon.com/Most-Incomprehensible-Thing-Introduction-Mathematics/dp/0957389450/ref=sr_1_1?s=books&ie=UTF8&qid=1475030510&sr=1-1&keywords=a+most+incomprehensible+thing

Not sure about the other topics, but if you really want to learn about the science of time dilation, I would recommend checking out Brian Greene's free courses on Special Relativity (either the conceptual one or the really math-centered one) and perhaps A Most Incomprehensible Thing by Peter Collier (a math-centered book that can potentially take the layman from high school mathematics to the equations of General Relativity).