Hill cipher
Encrypts blocks of letters by matrix multiplication modulo 26. Elegant algebra, and for exactly that reason transparent to anyone holding a little plaintext.
The mathematician Lester S. Hill published the method in 1929. Letters are mapped to the numbers 0–25, the plaintext is cut into blocks of n characters, and each block is multiplied by an invertible n×n matrix that serves as the key. Decryption uses the inverse matrix. It was the first practical cipher to treat more than three letters at a time as a single unit.
The trouble is that everything is linear. Given n matching pairs of plaintext and ciphertext blocks, the key is just a system of equations to solve. Hill went as far as building a mechanical device for six-letter blocks, but the cipher saw little real use. The idea of mixing a whole block through a matrix survives in AES's MixColumns step, this time sitting behind a non-linear S-box.