The term “Theatre of the Absurd” (also “Theater of the Absurd”) comes from an essay with that title, by Martin Esslin (1918-2002), in The Tulane Drama Review (May 1960). Esslin wrote:
   
“This common denominator that characterizes their works might well be described as the element of the absurd. ‘Est absurd ce qui n’a pas de but…’ ( ‘Absurd is that which has no purpose, or goal, or objective’ ), the definition given by Ionesco in a note on Kafka, certainly applies to the plays of Beckett and Ionesco as well as those of Arthur Adamov up to his latest play, Paolo Paoli, when he returned to a more traditional form of social drama.”
 
   
(Oxford English Dictionary)
Theatre of the Absurd  n. a collective term for plays (chiefly French) portraying the futility and anguish of man’s struggle in a senseless and inexplicable world (cf. absurd n.); also figurative.
1961   M. Esslin Theatre of Absurd 17   The Theatre of the Absurd strives to express its sense of the senselessness of the human condition and the inadequacy of the rational approach by the open abandonment of rational devices and discursive thought.
1962   Listener 13 Dec. 1027/1   The theatre of the absurd, whose master remains Camus.
   
Wikipedia: Theatre of the Absurd
The Theatre of the Absurd (French: théâtre de l’absurde [teɑtʁ(ə) də lapsyʁd]) is a post–World War II designation for particular plays of absurdist fiction written by a number of primarily European playwrights in the late 1950s. It is also a term for the style of theatre the plays represent. The plays focus largely on ideas of existentialism and express what happens when human existence lacks meaning or purpose and communication breaks down. The structure of the plays is typically a round shape, with the finishing point the same as the starting point. Logical construction and argument give way to irrational and illogical speech and to the ultimate conclusion—silence.
 
Etymology
Critic Martin Esslin coined the term in his 1960 essay “The Theatre of the Absurd”, which begins by focusing on the playwrights Samuel Beckett, Arthur Adamov, and Eugène Ionesco. Esslin says that their plays have a common denominator — the “absurd”, a word that Esslin defines with a quotation from Ionesco: “absurd is that which has not purpose, or goal, or objective.” The French philosopher Albert Camus, in his 1942 essay “Myth of Sisyphus”, describes the human situation as meaningless and absurd.
 
Wikipedia: Martin Esslin
Martin Julius Esslin OBE (6 June 1918 – 24 February 2002) was a Hungarian-born British producer, dramatist, journalist, adaptor and translator, critic, academic scholar and professor of drama, known for coining the term “theatre of the absurd” in his 1961 book The Theatre of the Absurd. This work has been called “the most influential theatrical text of the 1960s”.
     
Newspapers.com
27 April 1960, Los Angeles (CA) Times, pt. IV, pg. 11, col. 5:
Tulane University theater scholar Robert Corrigan will speak on the “Theater of the Absurd”—Beckett, Ionesco, Ganet and others—at 8 o’clock Friday night, Room 133, Founders Hall, SC.
 
OCLC WorldCat record
The Theatre of the Absurd
Author: Martin Esslin
Article, 1960
Publication: The Tulane Drama Review, 4, 19600501, 3
 
JSTOR
May 1960, The Tulane Drama Review, “The Theatre of the Absurd” by Martin Esslin, pg. 3:
The Theatre of the Absurd
By MARTIN ESSLIN
Pg. 4:
This common denominator that characterizes their works might well be described as the element of the absurd. “Est absurd ce qui n’a pas de but…” (“Absurd is that which has no purpose, or goal, or objective”), the definition given by Ionesco in a note on Kafka, certainly applies to the plays of Beckett and Ionesco as well as those of Arthur Adamov up to his latest play, Paolo Paoli, when he returned to a more traditional form of social drama.
Pg. 5:
Thus, the absurd and fantastic goings-on of the Theatre of the Absurd will, in the end, be found to reveal the irrationality of the human condition and the illusion of what we thought was its apparent logical structure.
Pg. 6:
The spectators of the Theatre of the Absurd are thus confronted with a grotesquely heightened picture of their own world; a world without faith, meaning, and genuine freedom of will. In this sense, the Theatre of the Absurd is the true theatre of our time.
     
OCLC WorldCat record
The Absurdity of the Absurd
Author: Martin Esslin
Article, 1960
Publication: The Kenyon Review, 22, 19601001, 670
 
Newspapers.com
7 May 1961, The Observer (London, UK), pg. 36, col. 1 ad:
THE UNIVERSITY OF HULL
DEPARTMENT OF ADULT EDUCATION
10th YORKSHIRE
SUMMER SCHOOL OF DRAMA
‘THE THEATRE
OF THE ABSURD’
 
OCLC WorldCat record
The theatre of the absurd. (Samuel Beckett, Eugène Ionesco, Arthur Adamov, Jean Genet, Edward Albee, Fernando Arrabal, Günter Grass, Harold Pinter, Norman Frederick Simpson)
Author: Martin Esslin
Print Book, Hungarian, [1961]
Publisher: doubleday Co XXIV, New York, [1961]
 
OCLC WorldCat record
Theatre of the Absurd, the
Author: Martin Esslin
Print Book, English, 1961
Edition: Revised Updated edition
Publisher: The Overlook Press, Woodstock, NY, 1961
 
Newspapers.com
9 November 1961, The Chapel Hill Weekly (Chapel Hill, NC), “Books” by Joe Nagelschmidt, pg. 18, col. 4:
THE THEATRE OF THE ABSURD, by Martin Eslin, is so-named, according to the book jacket because “The plays of Samuel Beckett, Eugene Ionesco, Arthur Adamov, Jean Genet, and a number of other avant-garde writers ... mark a new development in the contemporary theatre. Because its basic premise is the ultimate absurdity of the human condition ...” To be sure, there are no plays in this volume, it consists only of commentaries on the big absurdity, going back to the Keystone Kops and dadaism for early reference material. Excellent, for the serious student of theatre.