Since classical rhetoric, the four fundamental rhetorical operations, which still today serve to encompass the various figures of speech, have been: addition (adiectio), omission (detractio), permutation (immutatio) and transposition (transmutatio). Originally these were called, in Latin, the four operations of quadripartita ratio.
Latin origins 
The ancient surviving text mentioning them, although not recognizing them as the four fundamental principles, is the Rhetorica ad Herennium, of author unknown, where they are called ἔνδεια, πλεονασμός, μετάθεσις and ἐναλλαγή. Quintillian then mentioned them in Institutio Oratoria. Philo of Alexandria also listed them as addition (πρόσθεσις), subtraction (ἀφαίρεσις), transposition (μετάθεσις), and transmutation (ἀλλοίωσις).
Quintilian's perspective was to see rhetoric as the science of the possible deviation from a given norm, or from a pre-existing text taken as a model. Each variation can be seen as a figure (fugures of speech or figures of thought). From this perspective, Quintilian famously formulated four fundamental operations according to any such variation can be analyzed.
Reorganization by Groupe µ 
In 1970, the Belgian semioticians known under the name Groupe µ, reorganized the four operations. First they observed that the so-called transposition operation can be redefined as a series of addition and omission operations, so they renamed it as "omission-addition". They categorized the addition, omission and omission-addition operation as substantial operations, while they considered permutations as categorized permutation as relational operations.
They distinguished between partial and complete omissions; and between simple or repetitive additions. For an omission-addition operation, they considered it could be either partial, complete, or negative; a negative omission-addition operation is when it omits a unit and replaces it with its opposite.
Rhetoric of the image 
The Belgian semioticians known under the name Groupe µ, developed a method of painting research to apply the fundamental rhetorical operations in the interpretation of a work of painting. The method, called structural semantic rhetoric, aimed at determining the stylistic and aesthetic features of any painting through operations of addition, omission, permutation and transposition from a basic "zero degree" painting.
- Book IV, 21.29, pp.303-5
- Institutio Oratoria, Vol. I, Book I, Chapter 5, paragraphs 6 and 38-41. And also in Nook VI Chapter 3
- Harry Caplan
- Nöth (1990) pp.341,358
- Jansen (2008)
- James J. Murphy (2000) Grammar and rhetoric in Roman schools, in Sylvain Auroux (editor) History of the language sciences: An International Handbook on the Evolution of the Study of Language from the Beginnings to the Present, part XII, article 70, section 4, p.491
- Groupe µ (1970) A General Rhetoric, Introduction
- Groupe µ (1970) sections 3 to 3.2.1
- Winfried Nöth (1995) Handbook of semiotics pp.342, 459
- Jean-Marie Klinkenberg et al. (Groupe µ) (1980) Plan d'une rhétorique de l'image, pp.249-68
- Jansen, Jeroen (2008) Imitatio ISBN 978-90-8704-027-7 Summary translated to English by Kristine Steenbergh. Quote from the summary:
The variety of ways to adapt and enrich source texts, as discussed by Erasmus in De Copia Rerum, are discussed in chapter 5. [...] Classical rhetoric had already developed a theory of these kinds of intervention, drawing attention to the process of adaptation [...] If a topic had been treated by an earlier author, this was no reason to avoid it, but one had to try to emulate one’s predecessor. The use of rhetoric enabled authors to discuss the same topic in several ways, to be little a great subject, and to accord greatness to something small, for example, or to renew the old, and express the new in an old-fashioned manner. [...] Using these formulas, a pupil could render the same subject or theme in a myriad of ways. For the mature author, this principle offered a set of tools to rework source texts into a new creation. In short, the quadripartita ratio offered the student or author a ready-made framework, whether for changing words or the transformation of entire texts. Since it concerned relatively mechanical procedures of adaptation that for the most part could be learned, the techniques concerned could be taught at school at a relatively early age, for example in the improvement of pupils’ own writing.
- Nöth, Winfried (1990) Handbook of semiotics