Request for small textbook recommendations

You might enjoy the Very Short Introduction series, which is what it sounds like: short popular-level introductions to broad-ish topics, written by academics. Examples, to give a sense of the range:

• Global economic history
• Islam
• Human evolution
• Mathematics
• Documentary film

Entries are about 120 pages. Quality varies by the author - some can slip too far into academic jargon, but by and large they're decent (and cheap enough that it's no big loss if one turns out to be low-quality).

There's a series called "The Theoretical Minimum". These look like normal trade paperbacks and are mostly prose, but do in fact contain a lot of equations including some derivations and suggested exercises.

• Intro physics
• Quantum mechanics
• Special relativity
• General relativity

The KAM Story (about the KAM theorem in dynamical systems) bills itself as "a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists ... who are not experts in classical mechanics, and scientific-minded readers." I found this book super helpfully written because it is written for people at exactly my level. There's a glossary where definitions are given in mathematically formal terms, but not assuming that I already know all the background of the field. The text often refers to things quickly (and therefore efficiently) under the assumption that if I want to know more about it I can and will look it up.

Linear Algebra Done Right is a standard but small and highly-praised intro textbook on linear algebra.

The Mathematical Theory of Communication by Shannon and Weaver. It's an extended version of Shannon's original paper that established Information Theory, with some extra explanations and background. 144 pages.

JN Crossley, et al., What Is Mathematical Logic?

A 96-page intro to the basics of predicate calculus, model theory, and Gödel incompleteness. I've used it in the (distant) past a couple times when a student had trouble getting a practical grip on logic.

Are you opposed to PDFs or e-textbooks? I've found they're a huge benefit, it's all I use anymore.

Atiyah & McDonald's Introduction to Commutative Algebra fits. It's 125 pages long, and it's possible to do all the exercises in 2-3 weeks – I did them over winter break in preparation for a course.

Lang's Algebra and Eisenbud's Commutative Algebra are both supersets of Atiyah & McDonald, I've studied each of those as well and thought A&M was significantly better.

The Second Kind of Impossible, about the discovery of quasi-crystals. This one is also a standard sized trade paperback book, but it's fast to read because it's written in a way that is very engaging, while also going into a decent amount of technical detail.

IMMUNE, a book by the award-winning YouTube channel Kurzgesagt. It gets into a lot of mechanistic detail about how the immune system works while recognizing that you are a Normal Person who does not have time to learn organic chemistry. This one is not particularly short in length, but the readability makes up for it in time.

The Changing Brain: Alzheimer's Disease and Advances in Neuroscience. I read this a decade ago, but my recollection is that it was a highly readable narrative overview of the progress made in neuroscience (esp. Alzheimer's) in the '80s and '90s. It goes into a lot more detail than "here's what an action potential is", but not as much as a graduate textbook in neuroscience.

Foundations of the Theory of Probability is the definitive axiomatization of probability theory by Kolmogorov. It's very short at around 80 pages. I'm finding it a little hard to read because of old notation, but totally doable.