Autokey cipher
The autokey cipher starts from a short primer keyword and then extends the key with the message itself, so the key never repeats. In the plaintext variant the key continues with the plaintext; in the ciphertext variant it continues with the ciphertext just produced.
Break autokey without the primer
Paste ciphertext of at least 26 letters and the solver tries both variants over every primer length, keeping the decryption that reads as English. The plaintext variant is recovered exactly; in the ciphertext variant the opening letters are reconstructed from context.
About the autokey cipher
This is the cipher Blaise de Vigenère actually invented in 1586. The repeating-key cipher that carries his name is Bellaso's; history swapped the credit. By feeding the message back into the key, autokey removes the periodic repetition that Kasiski's attack and the index of coincidence exploit, which made it considerably stronger than the repeating-key cipher for three centuries.
It is not strong by modern standards. The plaintext variant chains errors but also chains information: guessing a probable word anywhere in the message extends the key around it, and statistical attacks that score candidate primers work well with computing power. The ciphertext variant is weaker still, since the key beyond the primer is public.