What are the best intro books for different science fields?

Here are some non-fictional books focused on STEM fields with STEM plots but are also good stories. They might serve as good introductions to then decide if you want to learn more about said topic:

“The Soul of a New Machine” by Tracy Kidder. In some respects outdated but still gives a great sense of what it’s like to design computers.

“The Cuckoo's Egg” by Clifford Stoll. A very fun read about finding a hacker in the early days of the Internet.

“Humble Pi” by Matt Parker. An extremely accessible book about math/engineering mistakes throughout history. He also has a great YouTube channel if you want to learn about math in a fun way.

I don't see any recommendations for linguistics, so I'll throw in my two cents there:

• Language Myths (a collection of chapters by various linguists) is the first linguistics book I'd recommend to any layperson. It's not necessarily teaching you linguistics per se, but it's dispelling widely-held misconceptions that are both incompatible with linguistics as a science and have real-world negative effects from people believing them. My first college intro class used it in addition to its other textbooks for that reason.

For good pop ling books, here are a couple I've liked:

• Because Internet by Gretchen McCullough is a great pop linguistics book that delves specifically into internet language
• Holy Sh*t: A Brief History of Swearing by Melissa Mohr is a good pop ling look into a more historical subject

As for actual introductions to the science of the field, I mostly had those in classes, but here are some introductory books I've heard recommended:

• Language: Its Structure and Use by Edward Finegan
• Contemporary Linguistics by William O'Grady et al.
• An Introduction to Language by Victoria Fromkin et al.
• Linguistics: An Introduction by Victoria Fromkin et al.

For introductions to specific subfields, again these are mostly recommendations I've heard around rather than ones I have firsthand experience with. These are generally going to be at a higher level than the preceding work, but hopefully still approachable once you've had a bit of basic exposure to the field as a whole. I'll try to put them in an ascending order of difficulty but I haven't read many of them myself so.

Phonology:

• Understanding phonology by Carlos Gussenhoven and Haike Jacobs
• Introductory Phonology by Bruce Hayes (we used excerpts from this in my class but fair warning that it's pretty old, so the theory is likely somewhat outdated)

Syntax & Morphology:

• Describing Morphosyntax by Thomas Edward Payne
• Understanding Morphology by Martin Haspelmath and Andrea Sims
• Understanding Syntax by Maggie Tallerman
• Thinking Syntactically: A Guide to Argumentation and Analysis by Liliane Haegeman
• The Syntactic Phenomena of English by James McCawley

Semantics & Pragmatics:

• Women, Fire and Dangerous Things by George Lakoff
• Understanding utterances by Diane Blakemore
• Everything that linguists have always wanted to know about logic (but were ashamed to ask) by James McCawley
• An introduction to meaning in natural language by Ronnie Cann et al.

Historical Linguistics:

• Understanding Language Change by April McMahon

Sociolinguistics:

• Introducing Sociolinguistics by Miriam Meyerhoff

I would recommend The Way Things Work Now by David Macaulay. It is presented as a children's book, but it has fantastic, intuitive explanations of all sorts of science and technology. Plus, there are mammoths.

Unrelated to the question, but the same author also wrote a book called Motel of the Mysteries which is a hilarious satire/critique of archeology.

I'm quite fond of Physics for Enquiring Minds: The Methods Nature and Philosophy of Science by Eric Rogers, which is old enough to be out of copyright and available for free on the internet archive.

The first couple paragraphs of the preface does a good job of laying out the goals and audience of the book:

This book offers a course in physics to non-physicists who wish to know physics and understand it. Here are the general reading, problems and laboratory instructions of a one-year course given at Princeton to undergraduates whose chief field of study lies outside technical physics: economists, students in humanities and in life sciences, and many premedicals. That course is open alike to those who have studied physics before and those who have not. Like that course, this book neither requires a previous physics course nor repeats in material or treatment the normal content of high-school physics -- so it welcomes all readers.
This book treats a series of topics intensively: topics chosen to form a coordinated structure of knowledge. Although mathematics provides the essential tools of physics, only the simpler parts of high-school algebra and plane geometry are used here. On the other hand, critical reading, good reasoning and clear thinking are asked for again and again. The problems, which are of primary importance are not plug-in slots for formulas, but ask for reasoning and critical thinking. In this way, both text and problems ask readers to learn by their own thinking.

Its a great book, highly recommended.

I also very much enjoy Calclus Made Easy: Being a very-simplest introduction to those beautiful methods which are generally called by the terrifying names of the Differential and Integral Calculus by Silvanus P. Thompson, also conveniently out of copyright, for which there is a very nice web version available at calculusmadeeasy.org which has my favorite epitaph of all time:

What one fool can do, another can (Ancient Simian Proverb.)

and also has a fantastic prologue:

Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks.
Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics — and they are mostly clever fools — seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.
Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.

Finally while we are on the topic of fantastic web versions of classic texts, checkout both the Feynman Lectures of Physics and the Structure and Interpretation of Computer Programs, though both of these texts, while introductions are targeting elite undergraduates.

Anyone have suggestions for Psychology? I'd like to have a better understanding of how my brain works.

Statistical inference: A commentary for the social and behavioural sciences, Michael Oakes. To compare the different statistical schools of thought, such as frequentist and Bayesian.

After the ice: A global human history

A great introduction to pre-history anthropology, it will delve into a story telling writing which helps review the scenarios with perspective. It also puts together different theories.

Feynman's books are good for basically a zero math intro (the ones like Six Easy Pieces, or the longer ones that are his edited full lectures) for physics. From there a decent AP or A level textbook would be good if you want to learn and practice some of the math. If you were truly daring you could go for an undergrad textbook....but I wouldn't recommend it since the math is significantly more intense as it involves calculus, vectors, and vector calculus. High school level tends to stick to algebra based physics.

If your algebra isn't great, I definitely recommend DragonBox Algebra 12+...it's a game, not a book, but is amazingly well done. Starts out as basic pattern/shape matching and eventually evolves into reasonably complex multivariable equations where you have to solve for x using basic math operations. Basically like a brain trainer, but purely algebra, and the game mechanics make the math "feel" more "tactile".

How to teach quantum physics to your dog is fantastic and doesn't require degree-level knowledge, but tries to give you an intuitive feel for quantum mechanics.

Alex's adventures in numberland is also fantastic, I remember reading both of these as a kid and they contributed to my desire to study physics at university.

Not book related, but a couple of online resources I love are Numberphile (maths), Sixty Symbols (physics), Periodic Videos (chemistry) and Computerphile (computer science) YouTube channels by journalist Brady Haran.

He goes to universities and asks their professors to explain what they study to a general audience (or if it's topical). Brady's so good as asking the kinds of questions the average person would have and catching the professor by surprise. He's also a big inspiration for me