I am ready to finish this off.
This is here to help you learn about the countertenor. It's intended to educate listeners rather than singers.
A countertenor is natural male voice that sings falsetto to allow him to sing music that was originally written for a woman or a castrato (a man castrated in childhood to retain his high voice, something that went on in the 17th and 18the centuries). In opera their use allows male roles to be sung by male singers, a feature that means nothing to me but seems to matter to others. Most countertenors are actually baritones. The voice range for a countertenor usually is the equivalent to a mezzo-soprano or contralto, but can include sopranos.
These are examples of roles written for the countertenor voice: Oberon in A Midsummer Night's Dream (Britten), Annas in Jesus Christ Superstar (Lloyd Webber), Akhnaten in Akhnaten (Glass), Trinculo in The Tempest (Adès), etc. Please notice that all these examples are modern, three out of four are British, and none of them are written by Italians.
This is David Daniels singing "I know a Bank" from A Midsummer Night's Dream.
David Walker sings Akhnaten's aria from Akhnaten.
Roles performed by countertenors but originally written for castrati include: Ariodante in Ariodante (Handel), Nerone in Agrippina (Handel), Ruggiero in Alcina (Handel), Giulio Cesare in Giulio Cesare (Handel), Artaserse and almost everyone else in Artaserse (Vinci), etc. All of these roles are also sung by women.
Franco Fagioli sings "Vo solcando un mar crudele" from Artaserse.
Philippe Jaroussky sings "Come Nube Che Fugge Dal Vento" from Agrippina.
A third category is roles composed for women which are then sung by countertenors. Sesto in Giulio Cesare is an example. This is uncommon.