Hybridity
One of the main themes of the play is that of creatures that are hybrids of different things; the title character, Hayavadana, is a hybrid of a man and a horse, and even Kapila and Devadatta end up being hybrids of each other. At the start of the play, being a hybrid is something godly and special; the opening prayer is to Ganesha, a god who is a boy with the head of an elephant. He is the lord and master of perfection which is paradoxical given his appearance. However, as the play continues, the hybrid characters seem less and less perfect to themselves and all ultimately feel that they are incomplete because they are not fully one creature or another.
Incompleteness
The theme of being incomplete is personified by all of the characters. Devadatta and Kapila are brain and brawn respectively, but neither feels truly complete. This is mirrored by Padmini; she chooses to take Devadatta as her husband but she still finds herself longing for the physicality of Kapila. She feels incomplete because she has been abandoned twice by the same two men, which emphasizes her own incompleteness to her.
Devadatta and Kapila feel a sense of incompletenes after they have each other's bodies joined to their own heads. At first it seems that Devadatta gets the best deal because he gets to keep his own sharp mind, and also has the muscular physique of Kapila. Kapila has his own strength of mind but has Devadatta's soft, unathletic body. He begins to feel incomplete as soon as the switch has occurred; however, when both men start to find that their bodies are returning to their prior state, they still both feel incomplete because they realize that they are living half existences.
The most obvious example of incompleteness is Hayavadana, who wants nothing more than to be made complete. He wants to be made fully a man but Kali makes him fully a horse instead. Even when she does so he feels incomplete because he still has the voice of a man. When he is able to change this and achieve the "neigh" of a horse instead he finally feels that he is complete.
Conflict Between Body and Mind
The play engages with the question of which is more powerful, the body or the mind. By all accounts it is the mind, as shown in Hayavadana, Devadatta, and Kapila's experiences, but Karnad also suggests the body has more power than one might initially assume. The body has memory, memory that stubbornly resists the mind's desire to sublimate it. The body's physical engagement with the world leaves a residue within, and when considering this as well as the putative supremacy of the mind, one must consider the two parts as near equals and both important to the formation of a complete identity.
Women's Subversiveness
Padmini might be a wife and mother, as traditional Indian society would dictate, but she is not complacent, quiet, or docile. She is a desiring, sensual women who pursues what—or who—she wants. She is openly selfish and independent-minded, something that the goddess Kali admires. Karnad allows her subversiveness to come through both her own words and those of the Female Chorus, which articulates her discontent with her conjugal life. Her sharp tongue and subtle subversiveness make her much more than a subaltern; rather, she is the closest to "complete" of all the characters.
City vs. Nature
Devadatta represents the city, a place dedicated to commerce and to the pursuits of the mind, not the body. The woods are associated woth Kapila in that they are a place where the physical body feels most at home, most complete. Nature is not opposed to the intellect, but it values strength, perseverance, and resilience; there the currency is not money but physical power. Padmini is a woman of the city but increasingly drawn to the woods, which represents her desire for both Devadatta and Kapila. Her son is naturally of both places, though, being raised in one and then the other, which suggests his identity will be more complete.
Theatre and Its Conventions
Karnad plays with the different levels of reality and drama throughout the piece. Bhagavata asks Ganesha for a blessing and speaks of the play's beginning, which is then interrupted by an Actor and Hayavadana. This is part of the play, though we are supposed to think it is not, and following it Bhagavata segues into a completely different story. A chorus and Bhagavata comment on the action, the latter speaking to and about the audience occasionally. And at the end, the two seemingly disparate plots suddenly converge, all done in a way to make the audience reflect on the didactic nature of theatre, the fusion and fragmentation of drama and real life, and the nature of storytelling.
Indian Identity
Karnad alludes to post-colonial India's identity problems through his characters, especially Hayavadana. After British rule, Indians were left with the vestiges of colonial politics, education, social structures, and more, which existed alongside and in tension with traditional Indian ones. Indians wrestled with their varying degrees of participation within the colonial system, and now in its vacuum had to come to terms with their fractured identity. By having Hayavadana try—and fail—to find completeness in purely Indian patriotic behavior, Karnad suggests how difficult this period is for his nation.