It would be good if one could separate these lists into free online material and links to online bookstores. Also, it would be nice to list popular and semi-formal material separate from real rigorous stuff, or to add some annotations to that effect.
Regarding quantum theory, these are the best introductory online materials I've found:
Quantum Mechanics and Philosophy: An Introduction by Ezio Vailati. (A gentle introduction, with lots of philosophical talk, but still presented using no-nonsense math.)
Consistent Quantum Theory by Robert Griffiths. (Rigorous, but limited to toy models in finite-dimensional Hilbert spaces. Presented using the consistent histories approach. Makes a good job of clarifying some points I found awfully confusing elsewhere.)
"Quantum Computing since Democritus" course notes by Scott Aaronson. (Lots of fun to read, semi-rigorous, touches on many computability/complexity/foundations topics.)
Also, general relativity isn't really discussed here much, but still, here are some online materials I can recommend, so you can consider adding that to the list:
Lecture notes by Stefan Waner. (Basic introduction, rigorous. The best free online text I've seen.)
Lecture notes by Sean Carroll. (Basic introduction, rigorous.)
Tutorial by John Baez. (A casual, semi-rigorous tutorial that developed out of an old online discussion. Excellent for building up intuitions when used alongside a more rigorous text.)
Lectures by Leonard Susskind. (Basic introduction, rigorous. A very good lecturer.)
Also, it would be nice to list popular and semi-formal material separate from real rigorous stuff, or to add some annotations to that effect.
I marked each item if it is either free and or easy now.
Update! New URL:
!!!
http://lesswrong.com/lw/2un/references_resources_for_lesswrong/
!!!
Out-of-date:
A list capturing all background knowledge you might ever need for LW.
Updated: 2010-10-10
This list has two purposes. One is to enable people that lack a basic formal education to read and understand the LessWrong Sequences. Secondly, it is meant as a list of useful resources for all people to help to better understand what is being discussed on LessWrong and to enable you to actively participate.
Do not flinch, most of LessWrong can be read and understood by people with a previous level of education less than secondary school. And even if you lack the most basic education, if you start with Khan Academy followed by BetterExplained then with the help of Google and Wikipedia you should be able to reach a level of education that allows you to start reading the LessWrong Sequences.
Nevertheless, before you start off you might read the Twelve Virtues of Rationality FE. Not only is scholarship just one virtue but you'll also be given a list of important fields of knowledge that anyone who takes LessWrong seriously should study:
Mathematics:
Basics
- The Khan Academy (World-class education for free (1800+ videos).) FE
- Just Math Tutotrials (FREE math videos for the world!) F
- BetterExplained (There’s always a better way to explain a topic.) FE
- Steven Strogatz on the Elements of Math (A very basic introduction to mathematics.) FE
GeneralLogic
Foundations
Game Theory
Programming:
Programming knowledge is not mandatory for LessWrong but you should however be able to interpret the most basic pseudo code as you will come across various snippets of code in discussions and top-level posts outside of the main sequences.
Python
for Python Games! F
Haskell
General
Computer sciences (General Introduction):
One of the fundamental premises on LessWrong is that a universal computing device can simulate every physical process and that we therefore should be able to reverse engineer the human brain as it is fundamentally computable. That is, intelligence and consciousness are substrate independent.
Machine Learning:
Not essential but an valuable addition for anyone who's more than superficially interested in AI and machine learning.
Miscellaneous:
Not essential but a good preliminary to reading LessWrong and in some cases mandatory to be able to make valuable contributions in the comments. Many of the concepts in the following works are often mentioned on LessWrong or the subject of frequent discussions.
Key Concepts:
Below a roundup of concepts and other fields of knowledge you should at least have a rough grasp of to be able to follow some subsequent discussions in the comments on LessWrong.
Note:
This list is a work in progress. I will try to constantly update and refine it.
Also thanks to cousin_it for the idea. I had to turn the original comment on his post into my own top-level post because I got the error that my comment was too long.
If you've anything to add or correct, please comment below and I'll update the list accordingly.