Polylphabetic
Use N substitution alphabets.
Periodical ciphers, with period N.
Example
Vigenère cipher.
Problems
Once known the period, is easy to cryptanalyze as N mono-alphabetic ones.
The period can be discovered using statistics.
Kasiski method.
Factoring of distances between equal ciphertext blocks.
Coincidence index.
Factoring of self-correlation offsets that yield higher coincidences.
Vigenère Cipher

Example of encryption of character M with key S, yielding cryptogram E.
Decryption is the opposite, E and S yield M.
Cryptanalysis of a Vigenère Cryptogram
Plaintext:

Cipher with the Vigenère square and key "poema"

Kasiski test
With the text above:

With the complete poem:

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