This chapter is devoted to post-quantum cryptography (PQC) concepts. Following the introduction, the following lattice-based cryptography concepts are described: module learning with errors (LWE)-based cryptography, ring LWE-based cryptography, lattice-based digital signatures, and lattice-based hash functions. The code-based cryptography concepts are described next including McEliece encryption scheme, Niederreiter cryptosystem, and quasi-cyclic (QC)-LDPC coding-based encryption. In the following section, the hybrid QKD-PQC concepts are introduced, in which the QKD and PQC are operated in a cooperative fashion. In this scheme, the raw key transmission is performed over QKD subsystem, while information reconciliation over the PQC subsystem. The following topics are described in this section: hybrid PQC-QKD encryption, spatially coupled LDPC coding-based McEliece encryption subsystem, and hybrid twin field (TF)-QKD-PQC encryption. The focus is then moved to the hash-based cryptography. After introducing the basic concepts from the hash-based cryptography including Lamport’s one-time signature scheme, two relevant schemes are described: Winternitz one-time signature (W-OTS) scheme and Merkle signature scheme (MMS) that is applicable to many-times signatures. After that we described relevant multivariate cryptography concepts.