Cryptographic hash functions are commonly used in many different areas of cryptography: in digital signatures and in public-key cryptography, for password protection and message authentication, in key derivation functions, in pseudo-random number generators, etc. Recently, cryptographic hash functions have received a huge amount of attention due to new attacks on widely used hash functions. This PhD thesis, having the title "Cryptographic Hash Functions", contains both a general description of cryptographic hash functions, including their applications and expected properties as well as some well-known designs, and also some design and cryptanalysis in which the author took part. The latter includes a construction method for hash functions and four designs, of which one was submitted to the SHA-3 hash function competition, initiated by the U.S. standardisation body NIST. It also includes cryptanalysis of the construction method MDC-2, and of the hash function MD2.