How is Leontes depicted in acts 1 and 2 of The Winter's Tale?

King Leontes is presented as a person deteriorating into false suspicion and paranoia as the first two acts unfold, leading him to crueler and crueler behavior.

At first, Leontes seems pleased with the visit of his childhood friend, now King Polixenes of Bohemia. However, the kind words about their friendship are spoken by Polixenes, who says to Hermione,

We were, fair queen
Two lads that thought there was no more behind
But such a day tomorrow as today
And to be boy eternal.

Leontes, however, shows he has a suspicious nature from the start, worrying that

his pond [is being] fished by his next neighbor, by
Sir Smile, his neighbor.

Nevertheless, Leontes asks Polixenes to stay longer. When that fails, he asks Hermione to ask Polixenes to lengthen his visit. When she does and he agrees (when he wouldn't to Leontes), Leontes explodes into jealousy and becomes convinced that Hermione and Polixenes are having an affair. Since Polixenes has been visiting for nine months, Leontes also becomes convinced that the pregnant Hermione is carrying Polixenes's child.

Leontes therefore asks one of his lords, Camillo, to poison Polixenes. Instead, Camillo warns Polixenes of his danger, and the two run off. This only further convinces the paranoid Leontes that Polixenes is guilty of sleeping with his wife. Leontes also, showing his increasing mental imbalance, accuses Polixenes of plotting against his life:

There is a plot against my life, my crown. All's true that is mistrusted.

Leontes imprisons his wife. No amount of pleading on her part will move him to believe her innocence. When their child is born, he wants it thrown into the fire, an act so cruel that it causes his courtiers to protest.

Leontes is a picture of man with too much power to indulge his paranoid fantasies. He has decided he knows what he knows, and no amount of argument is going to sway him. In fact, argument with him is futile: the more people plead innocence or plead that Hermione is innocent, the more this convinces Leontes that they are covering up her crimes. Since there is no one to hold him accountable, he is able to impose his false version of events on others and make them suffer as a result. His paranoia becomes a self-reinforcing loop.

Who is Leontes in Shakespeare's The Winter's Tale?

King Leontes of Sicily is the central character in The Winter’s Tale. In the play’s first half, an irrational jealousy possesses the king. He accuses his wife Hermione of having an affair with his best friend, King Polixenes of Bohemia. No one can convince Leontes of their innocence, and he goes so far as to plot the death of his friend and his wife’s newborn child. He forces Hermione to stand trial in court immediately after she gives birth in prison.

Leontes’s seeming madness results in the deaths of several people. His son Mamillius dies, supposedly of grief over being separated from his mother. When Antigonus agrees to abandon Hermione’s child in a remote location, he is eaten by a bear and the men on the ship drown in a storm. Leontes loses his son, his friend (who escapes back to Bohemia), his daughter, and his wife, whom the noblewoman Paulina reports as dead following her collapse.

The second half sees a repentant Leontes. Sixteen years have passed, and Leontes grieves daily, thinking of Hermione and his children:

Whilst I remember
Her and her virtues, I cannot forget
My blemishes in them, and so still think of
The wrong I did myself; which was so much,
That heirless it hath made my kingdom and
Destroy'd the sweet'st companion that e'er man
Bred his hopes out of.

These griefs have made Leontes a kinder person. When his daughter Perdita, who was found and raised by shepherds, escapes to Sicily with Polixenes’s son Florizel, Leontes welcomes them with open arms. He even reconciles with Polixenes. Because of this change in behavior, Paulina reveals, in the guise of a statue, that Hermione is still alive. Just as the play moves from winter to spring and tragedy to comedy, Leontes transforms from an angry and jealous husband into a compassionate father and friend.

In The Winter's Tale, how does Leontes transform throughout the play?

Very early in the play, Leontes is deeply loving towards his wife and his best friend. However, when he observes them seeming affectionate towards each other, he quickly turns violently jealous. Scholars have difficulty accounting for why this happens because there does not seem to be an outside motivation for it. Whatever the reason, Leontes' jealousy becomes more and more violent, such that he first arranges to murder his friend and then puts his wife on trial. He refuses to believe the Delphic Oracle when it says that Hermione is innocent. Only when Paulina reports that she is dead does he show regret. The play indicates that he mourns her and his actions for the next 16 years, portraying a humility he has never shown before. When she is revealed to be alive (or the statue of her comes to life, depending on your interpretation of the play) he is shocked and grateful.