How do Kryptologie, Kryptografie, and Kryptoanalyse relate to each other?

Cryptology is the umbrella discipline; cryptography is the constructive half (build secure schemes) and cryptanalysis is the destructive half (break them).

* Cryptology splits into cryptography (build secure schemes) and cryptanalysis (break them); cryptography splits again into symmetric and asymmetric. *

                  Kryptologie
                 /            \
        Kryptografie      Kryptoanalyse
        /         \
Symmetrische    Asymmetrische
Kryptografie    Kryptografie

• Kryptografie — designs and analyses systems for confidentiality, integrity, authenticity. Split into symmetric (shared secret key) and asymmetric (public/private key pair).
• Kryptoanalyse — studies attacks on cryptographic schemes: ciphertext-only, known-plaintext, chosen-plaintext, side-channel, etc. Both attackers and defenders need it: attackers to break; defenders to know what to defend against.

Tip: A textbook line — "a defender who doesn't understand cryptanalysis can't tell a secure scheme from a snake-oil one." That's why crypto courses cover attacks alongside constructions.

Go deeper:

• Cryptography (Wikipedia) — the whole field these two branches make up, and where symmetric vs asymmetric sit within it.