Notions of the Theatre of the Absurd as a cohesive or even self-aware movement are misleading. Unlike other significant avant-garde movements of the twentieth century, such as Surrealism, Bauhaus, Futurism or Dada, the Theatre of the Absurd had no manifesto, no formal ties between exponents. Although probably aware of one another's work, the playwrites now gouped together as absurdists did not work together. There was no specific political agenda behind these works, rather a common struggle to come to terms with fundamental, existentialist and metaphysical dilemmas.
The absurd condition can be loosely summed up as an attempt to find meaning in life when confronted with the omnipresent reality of death. All human exertions, it is suggested, are rendered absurd in light of their inevitable failure, and submission to the giggling dwarf (see Eugene Ionesco's The Killer) of death.
The Theatre of the Absurd was centered around Paris, the artistic capital of Europe for much of the twentieth century (arguably up until the riots of 1968). Of the four most significant playwrights of the absurd, Samuel Beckett, Eugene Ionesco, Jean Genet and Arthur Adamov, three were foreigners adopting Paris as their home, and French as their language of choice, and the other, Jean Genet, was French, but did not want to be (Genet eventually emigrated to America, and joined the Black Panthers. The sense of their otherness, and struggle against cultural hegemony appealed to his xenophile sensibilities).
The Theatre of the Absurd can profitably be seen as a theatre of the other. The themes of alienation, of the impotence of language as a medium for communication, and of the attempts to forge a new poetic, a new semantic system of the theatre are common between these works.
With despair and futility standing as central thematic pillars in the Theatre of the Absurd, one may be mistaken for anticipating works both painfully depressing and tedious. The truth is, however, that there is an almost omnipresent lightness of touch within these canons. Comedy is rife within these strange worlds. Beckett can often be seen as a playwrite of domestic comedy, condensed to almost crystalline purity. Ionesco's plays are as often hilarious as desperate.
Attempts to create existential theatre have not always been quite so successful - Sartre's No Exit, (also known as In Camera, or the original French Huis Clos) for example, whilst providing an interesting literary experiment (the play essentially functions as one long excuse to air the postulation that "hell is other people"), is almost unwatchably tedious.
If any of this sounds like your kind of kettle of fish, try checking out Samuel Beckett's Waiting for Godot, Eugene Ionesco's The Killer (it's a bit long, but persevere, it's worth it), Arthur Adamov's Parodie and Jean Genet's The Maids. Also, Martin Esslin's book, for an academic text, is highly readable, and well worth a visit.