Please post any sources that you would like to recommend or disclaimers you'd want stickied and if i said something stupid, point it out please.
Basic information for newcomers
There are two important laws in cryptography:
Anyone can make something they don't break. Doesn't make something good. Heavy peer review is needed.
A cryptographic scheme should assume the secrecy of the algorithm to be broken, because it will get out.
Another common advice from cryptographers is Don't roll your own cryptography until you know what you are doing. Don't use what you implement or invented without serious peer review. Implementing is fine, using it is very dangerous due to the many pitfalls you will miss if you are not an expert.
Cryptography is mainly mathematics, and as such is not as glamorous as films and others might make it seem to be. It is a vast and extremely interesting field but do not confuse it with the romanticized version of medias. Cryptography is not codes. It's mathematical algorithms and schemes that we analyze.
Cryptography is not cryptocurrency. This is tiring to us to have to say it again and again, it's two different things.
Resources
All the quality resources in the comments
The wiki page of the r/crypto subreddit has advice on beginning to learn cryptography. Their sidebar has more material to look at.
github.com/pFarb: A list of cryptographic papers, articles, tutorials, and how-tos - seems quite complete
github.com/sobolevn: A list of cryptographic resources and links -seems quite complete
u/dalbuschat 's comment down in the comment section has plenty of recommendations
this introduction to ZKP from COSIC, a widely renowned laboratory in cryptography
The "Springer encyclopedia of cryptography and security" is quite useful, it's a plentiful encyclopedia. Buy it legally please. Do not find for free on Russian sites.
CrypTool 1, 2, JavaCrypTool and CrypTool-Online: this one i did not look how it was
*This blog post details how to read a cryptography paper, but the whole blog is packed with information.
Overview of the field
It's just an overview, don't take it as a basis to learn anything, to be honest the two github links from u/treifi seem to do the same but much better so go there instead. But give that one a read i think it might be cool to have an overview of the field as beginners. Cryptography is a vast field. But i'll throw some of what i consider to be important and (more than anything) remember at the moment.
A general course of cryptography to present the basics such as historical cryptography, caesar cipher and their cryptanalysis, the enigma machine, stream ciphers, symmetric vs public key cryptography, block ciphers, signatures, hashes, bit security and how it relates to kerckhoff's law, provable security, threat models, Attack models...
Those topics are vital to have the basic understanding of cryptography and as such i would advise to go for courses of universities and sources from laboratories or recognized entities. A lot of persons online claim to know things on cryptography while being absolutely clueless, and a beginner cannot make the difference, so go for material of serious background. I would personally advise mixing English sources and your native language's courses (not sources this time).
With those building blocks one can then go and check how some broader schemes are made, like electronic voting or message applications communications or the very hype blockchain construction, or ZKP or hybrid encryption or...
Those were general ideas and can be learnt without much actual mathematical background. But Cryptography above is a sub-field of mathematics, and as such they cannot be avoided. Here are some maths used in cryptography:
Finite field theory is very important. Without it you cannot understand how and why RSA works, and it's one of the simplest (public key) schemes out there so failing at understanding it will make the rest seem much hard.
Probability. Having a good grasp of it, with at least understanding the birthday paradox is vital.
Basic understanding of polynomials.
With this mathematical knowledge you'll be able to look at:
Important algorithms like baby step giant step.
Shamir secret sharing scheme
Multiparty computation
Secure computation
The actual working gears of previous primitives such as RSA or DES or Merkle–Damgård constructions or many other primitives really.
Another must-understand is AES. It requires some mathematical knowledge on the three fields mentioned above. I advise that one should not just see it as a following of shiftrows and mindless operations but ask themselves why it works like that, why are there things called S boxes, what is a SPN and how it relates to AES. Also, hey, they say this particular operation is the equivalent of a certain operation on a binary field, what does it mean, why is it that way...? all that. This is a topic in itself. AES is enormously studied and as such has quite some papers on it.
For example "Peigen – a Platform for Evaluation, Implementation, and Generation of S-boxes" has a good overviews of attacks that S-boxes (perhaps The most important building block of Substitution Permutation Network) protect against. You should notice it is a plentiful paper even just on the presentation of the attacks, it should give a rough idea of much different levels of work/understanding there is to a primitive. I hope it also gives an idea of the number of pitfalls in implementation and creation of ciphers and gives you trust in Schneier's law.
Now, there are slightly more advanced cryptography topics:
For those topics you'll be required to learn about:
At that level of math you should also be able to dive into fully homomorphic encryption, which is a quite interesting topic.
If one wish to become a semi professional cryptographer, aka being involved in the field actively, learning programming languages is quite useful. Low level programming such as C, C++, java, python and so on. Network security is useful too and makes a cryptographer more easily employable. If you want to become more professional, i invite you to look for actual degrees of course.
Something that helps one learn is to, for every topic as soon as they do not understand a word, go back to the prerequisite definitions until they understand it and build up knowledge like that.
I put many technical terms/names of subjects to give starting points. But a general course with at least what i mentioned is really the first step. Most probably, some important topics were forgotten so don't stop to what is mentioned here, dig further.
There are more advanced topics still that i did not mention but they should come naturally to someone who gets that far. (such as isogenies and multivariate polynomial schemes or anything quantum based which requires a good command of algebra)
