If you want to find examples of multiple ironies in this excellent story, you need look no further than the relationship between the two central characters, Gurov and Anna, his mistress. Gurov starts off the story as an idle dilletante who is endowed with the ability to casually seduce women. He sees Anna as just another diversion or dalliance, wanting to have his fun then return to his life back in Moscow. However, little does he know that ironically this relationship will develop into something much more serious, not just a dalliance at all.
Likewise, this relationship will actually be the source of Gurov's transformation. Note how at the start of the story he patronisingly dismisses women as "the lower race." Yet as we can see through his developing love and friendship for Anna that he is transformed and accepts her as an equal.
Lastly, it is ironic that Anna and Gurov only find each other when they are both already married and Gurov himself is aging and not getting any younger. Note what Gurov thinks about his relationship:
He and Anna Sergeyevna loved one another as people who are very close and intimate, as husband and wife, as dear friends love one another. It seemed to them that fate had intended them for one another, and they could not understand why she should have a husband, and he a wife. There were like two migrating birds, the male and the female, who had been caught and put into separate cages.
How ironic that Anna Sergeyevna, who was viewed just as one of many "diversions" for Gurov, should develop into so much more, should be responsible for Gurov's moral transformation and should actually be the "wife" of Gurov that he has been waiting for all his life!