I've read a couple of Sean Carroll's pop-science books (The Big Picture and Something Deeply Hidden) over the past few years, so when this new one became available at Portsmouth Public Library, I grabbed it.
Now, science books aimed at the masses will often shy away from math. Sometimes their authors will acknowledge and excuse this by pointing out the relevant market forces: their publishers' research shows that each equation in a book will decrease sales by X percent, or something. But (I assume) Carroll successfully persuaded his publisher to let him math it up in this book, so good for him. This book is volume one of a projected trilogy; the next one will be subtitled Quanta and Fields, and the last Complexity and Emergence. I'm on board.
But this book concentrates on "classical" physics. He starts off slow, describing Newtonian mechanics, conservation laws, aided by basic calculus. Moving on to Lagrangian mechanics and the principle of least action. And then Hamiltonian mechanics. All do an approximately fine job of describing non-relativistic motion of macroscopic bodies.
But then we edge into Einsteinian insights, the interplay between space, time, mass, and energy. And then (watch out!) the notion of curved spacetime, which quickly invokes (eek!) tensor notation, the better to introduce General Relativity. And before you know it, we're hip deep in Riemann and Ricci and all that stuff. To a point where (if you've been following along, nodding your head) you can appreciate beauty of the Einstein equation (I'm not sure how this will appear on Goodreads):
Rμν - ½Rgμν = 8πGTμν
And we wind up with a good (but quick) discussion of black holes (they're hairless!), event horizons, naked singularities, accretion disks, gravitational waves and the like.
I must confess that, even though I was a physics major decades ago, I got lost at a certain point. I think to actually know this material, you have to take courses from smarter people, doing problem sets along the way. There's no shiny magic path to understanding. But (on the other hand) I learned a good deal at the fuzzy territory between "yeah, this is simple, I get this" and "whoa, what's going on here?"