Calculus

• Thomas' Calculus by Hass, Heil, and Weir (I learned calculus with this book)
• Paul's Online Math Notes (Calculus I, Calculus II, Calculus III)
• Calculus by Stewart
• Schaum's Outline of Calculus by Ayres and Mendelson

(Ordinary) Differential Equations

• Differential Equations and Boundary Value Problems by Edwards, Penney, and Calvis
• A First Course in Differential Equations by Dennis Zill
• Ordinary Differential Equations by Morris Tenenbaum
• Paul's Online Math Notes Differential Equations (here)

Proofs

• Book of Proof by Richard Hammack (can be found here for free from the author) [My review]
• Naive Set Theory by Paul Halmos (not really a proofs book, but it certainly helped me learn proof concepts)

Linear Algebra

• [Computational and Proof] Elementary Linear Algebra by Stephen Andrilli and David Hecker (I learned proof based LA with this one)
• [Computational] Elementary Linear Algebra by Howard Anton
• [Proof] Linear Algebra Done Right by Sheldon Axler
• [Proof] Linear Algebra by Friedberg, Insel, and Spence

Analysis

• Basic Analysis I by Jiri Lebl (can be found here for free from the author)
• Elementary Analysis: The Theory of Calculus by Kenneth Ross
• Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings
• Understanding Analysis by Stephen Abbott
• Elementary Real Analysis by Thomson, Bruckner, and Bruckner (treats single, multivariable, and metric spaces. Can be found here.)

Abstract Algebra

• Abstract Algebra: An Introduction by Hungerford (a word of warning: this book is unconventional in the sense that it starts with ring theory, develops fields, and then goes into group theory towards the end. Most books do not do this, but I found it more approachable.)
• Abstract Algebra: Theory and Applications by Judson (can be found here for free from the author)
• Basic Abstract Algebra for Graduate Students and Advanced Undergraduates by Robert Ash (has full solutions to all problems and is a Dover book!)

Partial Differential Equations

• Applied Partial Differential Equations with Fourier Series and Boundary Value Problems by Richard Haberman
• Partial Differential Equations for Scientists & Engineers by Stanley Farlow

Fourier Analysis

• Fourier Series by Georgi Tolstov
• Fourier Analysis: An Introduction by Stein and Shakarchi

Calculus of Variations

• Calculus of Variations by Gelfand and Fomin
• Calculus of Variations: with Applications to Physics and Engineering by Robert Weinstock
• Calculus of Variations by Lev Elsgolc

Numerical Analysis

• A First Couse in the Numerical Analysis of Differential Equations by Arieh Iserles (This book was tough for me without the help of my professors lecture notes/explanations. I think it requires a certain level of mathematical maturity.)
• Numerical Methods for Engineers by Chapra and Canale (much more approachable than the Iserles book, but it is not written for mathematicians unlike the Iserles book)

Differential Geometry

• A Course of Differential Geometry and Topology by A. Mishchenko and A. Fomenko (Mir Publishers Moscow)
• Differential Geometry by Erwin Kreyszig

Measure Theory

Okay, while I have not studied measure theory formally, I plan on doing so using the following book(s). I have the hardcover version, but if you can learn from PDFs well enough, then Axler's book is a good option.

• Measure, Integration, and Real Analysis by Sheldon Axler (can be found here for free from the author)
• Real Analysis by Royden

General Interest

• Infinite Powers: How Calculus Reveals the Secrets of the Universe by Steven Strogatz
• A Student's Guide to Laplace Transforms by Daniel Fleish
• All the Mathematics You Missed: But Need to Know for Graduate School by Thomas Garrity
• The Joy of X: A Guided Tour of Math, from One to Infinity by Steven Strogatz

General Physics

• Sears and Zemansky's University Physics with Modern Physics by Young and Freedman (I used this to learn physics)
• Fundamentals of Physics by Halliday, Resnick, and Walker (I haven't used this, but have heard many good things)

Engineering Statics

• Engineering Mechanics: Statics by Russell Hibbeler

Engineering Dynamics

• Engineering Mechanics: Dynamics by Russell Hibbeler

Mechanics of Materials

• Mechanics of Materials by Russell Hibbeler
• Schaum's Outline of Strength of Materials by Merle Potter

Classical Mechanics

I haven't taken a classical mechanics course, but I used Taylor's text on my own to learn Lagrangian mechanics and some stuff about vibrations. I found it to be very easy to read.

• Classical Mechanics by John R. Taylor
• Introduction to Classical Mechanics by David Morin

Quantum Mechanics

I want to learn quantum mechanics very badly, but have not had the time to dive into it. These are the books I own and plan to use to accomplish that goal. I have seen glowing reviews for these and so I believe in their value.

• Introduction to Quantum Mechanics by David Griffiths (a gentler text for undergrads)
• Principles of Quantum Mechanics by Shankar (this one looks really good!)
• Modern Quantum Mechanics by Sakurai (pretty sure this is more of a grad level book. I don't own this one yet.)

Thermodynamics

• Fundamentals of Engineering Thermodynamics by Moran and Shapiro (I read nearly every word of this book and really liked it!)

Fluid Mechanics

• Munson, Young, and Okiishi's Fundamentals of Fluid Mechanics by Gerhart, Hochstein, and Gerhart
• Schaum's Outline of Fluid Mechanics by Potter and Wiggert

Heat Transfer

• Fundamentals of Heat and Mass Transfer by Bergman and Lavine

Nuclear Engineering

These are ones that I have perused a bit, but want to study in detail in the future. So far, I have only made it through Ch. 1 of the first two :/.

• Fundamentals of Nuclear Science and Engineering by Schultis and Faw
• Nuclear Reactor Engineering: Reactor Design Basics 4ed Vol I by Glasstone and Sesonske
• DOE Fundamentals Handbook: Nuclear Physics and Reactor Theory Volume I of II (download this here)
• DOE Fundamentals Handbook: Nuclear Physics and Reactor Theory Volume II of II (download this here)

Biographies

• Marine Sniper: 93 Confirmed Kills by Charles Henderson
• War Shots: Norm Hatch and the US Marine Corps Combat Cameramen of World War II by Charles Jones and James Jones (see the footage Norm Hatch captured here on YouTube)

Chemical Weapons

• The Chemical Warfare Service: From Laboratory to Field by U.S. Army Center of Military History

General

• The Pentagon's Brain: An Uncensored History of DARPA, America's Top Secret Military Research Agency by Annie Jacobsen
• The Art of Intelligence: Lessons from a Life in the CIA's Clandestine Service by Henry Crumpton

Memoirs

• Skunk Works: A Personal Memoir of My Years at Lockheed by Ben Rich
• One Bullet Away: The Making of a Marine Officer by Nathaniel Fick
• Shady Lady: Flying the 'Dragon Lady' U-2 Spy Plane by Rick Bishop
• The Guerrilla Factory: The Making of Special Forces Officers by Tony Schwalm

Nuclear Weapons

• Command and Control: Nuclear Weapons, the Damascus Incident, and the Illusion of Safety by Eric Schlosser
• 15 Minutes: General Curtis LeMay and the Countdown to Nuclear Annihilation by L. Douglas Keeney
• Nuclear Strategy in the Modern Era: Regional Powers and International Conflict by Vipin Narang
• The Logic of American Nuclear Strategy: Why Strategic Superiority Matters by Matthew Kroenig
• Nuclear War Survival Skills by Cresson H. Kearny (from Oak Ridge Nat'l Laboratory)
• Tactical Nuclear Weapons: Emergent Threats in an Evolving Security Environment by Brian Alexander
• The Effects of Nuclear Weapons, 3rd Edition by Samuel Glasstone and Philip Dolan [online version here]

Submarines

• Blind Man's Bluff: The Untold Story of American Submarine Espionage by Sherry Sontag and Christopher Drew with Annette Lawrence Drew
• The Hunt for Red October by Tom Clancy (yeah, I know it's fiction but c'mon, it's a classic for a reason!)

Russian Literature

• Anna Karenina by Leo Tolstoy [currently reading, 12/4/24]
• Crime and Punishment by Fyodor Dostoyevsky
• How Much Land Does a Man Need by Leo Tolstoy
• The Overcoat by Nikolai Gogol
• White Nights by Fyodor Dostoyevsky

Fanstasy

• Game of Thrones by George R.R. Martin