Kyber is a lattice-based key encapsulation mechanism (KEM). Dilithium is a lattice-based digital signature algorithm (DSA). Both have been standardized by the National Institute of Standards and Technology (NIST) as part of their post-quantum cryptography initiative. NIST published the final standards on 13 August 2024, renaming Kyber to ML-KEM (FIPS 203) and Dilithium to ML-DSA (FIPS 204), and told administrators to start integrating them immediately instead of waiting for future standards.
Alfred Menezes offers a comprehensive introduction to both quantum-safe cryptographic schemes. The course is structured into four video lectures: an introduction with the mathematical prerequisites, Kyber, Dilithium, and the Number-Theoretic Transform used by both. The stated goal is that you can read FIPS 203 and FIPS 204 afterwards, including the details the lectures leave out. Homework you will actually want to do, for once.