Affected Homage
When Professor Preobrazhensky first takes Sharik back to his apartment, he welcomes him in by saying, “Come in, please, Mr. Sharik" (13). While the professor is said to do this "ironically" insofar as he is paying undue respect to a mongrel he found on the street, the true irony here lies in the fact that Sharik will, in fact, become a gentleman through the professor's experiment. This ironic comment thus also represents an example of foreshadowing in the text.
The Experiment
The experiment conducted on Sharik presents a case of situational irony. While Professor Preobrazhensly and Dr. Bormenthal thought that, by transplanting the hypophysis and testes of another person into Sharik, they could test the rejuvenatory properties of these organs, what they actually found was that these two organs contain the anatomical and personal information needed to produce a human from scratch. This central irony is what allows Sharik to become Polygraph Polygraphovich and annoy the professor greatly until they reverse the procedure.
Professor Preobrazhensky
Professor Preobrazhensky is a very ironic figure insofar as he is guarded by the same establishment whose ideals he so openly contradicts. He spreads anti-Bolshevik rhetoric in private to his friends and clients, occupies far more space with his apartment than the average Russian citizen, and disdains the upsetting of the Tsarist order, taking care to maintain the decorum and manners of the old aristocracy. A major irony within the text, then, is that each time someone tries to bring him down for this anti-Bolshevik behavior, he is shielded from within the regime itself (e.g., his friend who tells him of Sharik's accusations, his friend in charge of the housing committee who tells Shvonder to stand down).
The Solution
There is also a great deal of irony in how the main plot of the story resolves. So much of the professor's pain in the story is caused by his reluctance to rid himself of the human Sharik/Polygraph Polygraphovich. While the professor detests his creation, he also recognizes the scientific value that his creation has as a testament to the efficacy of the transplant procedure. Ironically, however, when the stress of living with human Sharik becomes too great, the professor takes a self-contradictory action—that is, reversing the procedure and wiping his achievement out in order to return his lifestyle before the procedure was ever performed. The scientist is made to advocate against the overreach of science, and he even argues at length with Dr. Bormenthal about how the natural order ought to be left alone, since Nature provides more than enough geniuses and great men on her own.