Don Quixote tells the story of a character whose mission is to return chivalry to the world. The main character of the book is portrayed as clumsy and delusional and he often fails (comically) in this quest. In this sense, he is very human, very relatable. He is not a superhero or a trained knight who can defeat many enemies like in other tales of knights in shining armor. The word quixotic is defined as exceedingly idealistic, unrealistic and impractical.
A good research topic would be to compare the mission of Don Quixote to real life persons of past and present. What are some real-life examples of a seemingly insurmountable problem being taken head on by on optimistic person regardless of his abilities? How does mainstream society perceive people who try to change the world by preaching a message that goes against the status quo? For example, nobody thought that Gandhi could change the world through peace and by loving your enemies.
Another topic could be a commentary on the effectiveness of a quixotic outlook. For instance, do you relate more to Don Quixote, or those that called him a fool, or perhaps a combination of both? Don Quixote lived in a different time. How would a character like him be received today?
An interesting example can be taken from HBO's hit series The Newsroom. The main character is a television journalist who is on a 'quixotic' mission to restore a sense of integrity to modern journalism. In a world of 24-hour news cycles and news programming that seeks to entertain rather than inform the American public, the main character is trying to change the status quo, to restore chivalry to the field in the same way as Don Quixote does. The main character in The Newsroom quotes the novel on several occasions throughout the series.