One theme is redemption. Describe two examples of this theme from the story.

I disagree redemption is a theme in the story because the
evidence for it is too weak.  The strongest example is of Sirius's case, but (1) he
was innocent of wrongdoing that needs forgiveness, and (2) few people finally understand
his innocence (while almost everyone continues to wrongly view him as deserving a
Dementor's kiss).  Similarly, Buckbeak and Crookshanks do no wrong that they need
redemption for.  As Hermione points out about her cat, he "doesn't understand it's
wrong!"  Animals act on instinct, so it makes no sense to apply human moral judgments to
their actions.  The same is true of Buckbeak's attack on Malfoy when he is provoked by
that git's insult.  As Hagrid understands, it is the nature of Hippogriffs to be proud
and respond viciously to an offense; they can't help it.  The examples of the animals in
the story help illustrate what's different about cruel behavior by humans: we have a
concept of morality and can choose how we act.  With Buckbeak, we can say revenge is
natural and not question the justice of clawing Malfoy to avenge mere insulting words. 
For humans, it not so simple.

Another problem with the idea
of redemption as a theme is that it understands the term very narrowly.  Sirius and
Buckbeak are simply rescued from others' cruelty and injustice, so it would be more
precise to say simply that the theme of the story is "being rescued," which sounds
ridiculous.  "Redemption" can also mean (1) atonement for guilt or (2) deliverance from
sin; but neither of these meanings make sense in relation to Sirius, Buckbeak, or
Crookshanks.  

Furthermore, it is always vague and
reductive to speak of a theme using just one word.  A theme is an important idea
suggested in a story, not a general subject.  People often confuse "theme" and
"topic," perhaps partly because it is much easier to speak vaguely than it is to be
precise.

With regard to this story, the main theme
certainly has to do with revenge.  The theme could be stated in different ways, but it
might be expressed as the idea that revenge is cruel and unjust.  How many characters in
this story have "got it in for" somebody?  In addition to his usual grudge against
Harry, Snape has it in for Neville, Lupin, and Sirius--even to the extent of wanting
to kill Sirius to avenge a stupid prank played in school.  Buckbeak takes revenge on
Malfoy.  Malfoy takes revenge in turn by trying to get Hagrid sacked and Buckbeak
killed.  The Ministry wants to punish Sirius with a Dementor's kiss, an extremely evil
sort of weapon that Lupin suggests nobody could really deserve.  When Harry learns that
his parents were betrayed to their deaths by Black, even he broods on revenge and thinks
he deserves the Dementor's kiss.  Yet, we learn that they are all wrong in judging
Sirius, and also that it can be extremely difficult to convince people of the truth.  As
Dumbledore says, even he has no power to do this.  The story shows how ignorant people
are and prone to mistakes of judgment, and that those mistakes are often prompted by
personal motives such as pride, fear, and hatred.

In the
end, Harry stops Lupin and Sirius from killing Pettigrew even though the latter is an
utterly despicable person who is unquestionably guilty of murdering numerous
people. Harry doesn't forgive Pettigrew.  As he says, he doesn't want his father's
best friends to be killers.  Revenge is not justice.