While this SE site is a good source for getting specific questions answered, where can I go to gain good background knowledge and learn technical details about Monero?
5 Answers
A good place to start would be https://getmonero.org/home, try looking at the various topics under Knowledge Base. If you have further specific questions, you can ask on Reddit, IRC, or here.

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There's a pretty solid introductory website over at http://moneroinfo.org. I typically point people there if they are completely brand new.
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That page doesn't load for me... – user141 Oct 11 '16 at 23:02
Here! Just ask what you would like to know, or browse the other questions. Searching by tags is a useful way to find a lot about a certain topic.

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The best information can still be found on the CryptoNote website. (CryptoNote is a cryptocurrency platform from which Monero descends.)
You can find a well-illustrated explanation of the general principles here: https://cryptonote.org/inside/
Low-level technical descriptions/standards can be found here: https://cryptonote.org/standards/
Note that Monero is more and more diverging from this, so not everything will apply directly. The overall principles are the same, though - at least until Confidential Transactions (CT) is deployed in Monero.

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I would also suggest a peek at https://getmonero.org/research-lab/
This page has links to the CN whitepaper, the CN whitepaper annotated by the MRL team and a full review by Surae Noether.
It also links you to https://lab.getmonero.org/

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