The four Quagmires
Quagmire ciphers are Vigenère ciphers where the alphabets are scrambled with a keyword. Quagmire I scrambles the plaintext alphabet, II scrambles the ciphertext alphabet, III uses the same scrambled alphabet for both, and IV uses two different scrambled alphabets. An indicator key, like Vigenère's key, slides the cipher alphabet for each letter.
By convention, each indicator letter lines up under plaintext A for types I and II, and under the first letter of the keyed plaintext alphabet for III and IV. If a puzzle uses a different alignment, enter that plaintext letter in the last box.