The Gronsfeld cipher is a polyalphabetic substitution cipher, whereby plaintext letters are shifted by a number of places in the alphabet according to digits in a key number (like a PIN). For example, given a key "1024", the plaintext word "cipher" would be enciphered as follows (assuming the standard 26-letter alphabet):
The Gronsfeld cipher is used in Jules Verne's La Jangada (known as Eight Hundred Leagues on the Amazon in English) and several other fictions. Similar ciphers actually used in the 19th century are described in Etienne Baserie (1901), Les Chiffres Secrets Dévoilés.
The Gronsfeld cipher is so called because Gaspar Schott (aka, Kaspar Schott or Caspar Schott in German and Gaspar Schottus in Latin) (Wikipedia) (1608-1666) described it as what he learned from the Count of Gronsfeld (aka, Graf von Gronsfeld in German, Comes [Comite in ablative] à Gronsfeld in Latin).
Among many works of Gaspar Schott, the reference is found in Magia universalis naturae et artis (1658-1659) (Linda Hall Library, a 1677 edition at Google, another copy), Part IV (1659), which consists of Book I "Magia Cryptograhpica & Cryptologica" (p.1-92), Book II "Magia Pyrotechnica", Book III "Magia Magnetica", Book IV "Magia Sympathica & antipathica", Book V "Magia Medica", Book VI "Magia divinatoria", Book VIII "Magia Chiromantica". It gives (p.65-69) the following example with a key "436":
(In shifting by the specified number of places in the alphabet, the plaintext letter itself is counted in this example. For example, "b" is shifted to "D" with a key "3". As was usual at the time, the alphabet consisted of 24 letters, with no distinction between i and j and between u and v. Further, "w" is placed after "x-y-z", as is shown by "t" being shifted to "W" with a key 6 and also as seen in the explicit listing on p.70.)
(I think the above pages are the ones referenced in Karl de Leeuw et al. (ed.), The History of Information Security (2007), 220.127.116.11 (p.309, n.66) (this also discusses other related works of Schott). On the other hand, David Kahn, The Codebreakers (1967) cites "Magia universalis ... (Nuremberg, 1659), IV, 33" and says that the Count of Gronsfeld described the scheme to Schott "while they went together from Mainz to Frankfort" (p.245 and its endnote). I have not yet located the source of this additional information.)
The source of Gaspar Schott is probably Jost Maximilian [aka, Josse Maximilien, Justus Maximiliaan] von Bronckhorst-Gronsfeld [Gronsveld in Dutch] (German Wikipedia).
The article on "Gronsfeld-Chiffre" in German Wikipedia attributes the scheme to his son (Wikipedia) Johann Franz von Gronsfeld (1640-1719), who, however, seems too young, given the fact that the reference to the count already appeared in Part I (1658) of Magia universalis.
Polyalphabetic substitution with a keyword per se was described by Giovan Battista Bellaso as early as 1553 but, as far as I know, what is known today as the Vigenere cipher or the Gronsfeld cipher was not described in his works. Still, according to Romano Sarzi, Ziffre dei Gonzaga, Part 2 (pdf), the scheme of the Gronsfeld cipher was employed in a cipher prepared for Silvio Calandra (c.1540-1590), ambassador of the Duke of Mantua and involved in diplomatic missions with Savoy and Milan in 1560s-1570s until his downfall in 1579 (Dizionario Biografico dgli Italiani vol.16). The example given is as follows:
(The shifting is in the opposite direction from the examples given above.)
The Gronsfeld cipher is theoretically a reduced version of the Vigenere cipher. The Vigenere cipher switches among the 26 substitution alphabets according to the letters in a keyword, whereas the Gronsfeld cipher can be viewed as switching among the 10 substitution alphabets (i.e., the 10 alphabets shifted by 0 to 9 places) according to the digits in a key number (like a PIN).
However, people who used the Gronsfeld scheme may have simply (re)invented it as a natural extension of the Caesar cipher. In the Caesar cipher, every plaintext letter is shifted by an arbitrary (but fixed) number of places, whereas the Gronsfeld cipher varies the number of places of the shift for every plaintext letter. (Strictly speaking, it is not an "extension" because the shift is limited to the range of 0 to 9 in the Gronsfeld cipher.)
Thus, it would not be surprising if there were other people who devised this scheme independently of the Count of Gronsfeld.