Hill Cipher is a polygraphic substitution cipher based on linear algebra. Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once. It used matrices and matrix multiplication to mix up the plaintext.

Homophonic Substitution Cipher is a substitution cipher in which single plaintext letters can be replaced by any of several different ciphertext letters. They are generally much more difficult to break than standard substitution ciphers.

Playfair Cipher is a manual symmetric encryption technique and was the first literal digram substitution cipher. It encrypts pairs of letters (bigrams or digrams), instead of single letters as in the simple substitution cipher and rather more complex Vigenère cipher systems then in use.

Polybius Square Cipher is essentially identical to the simple substitution cipher, except that each plaintext character is enciphered as 2 ciphertext characters. It can ususally be detected if there are only 5 or 6 different characters in the ciphertext.