If you are writing a summary about something that you've read, a teacher will almost ALWAYS want that summary to be objective and third person, meaning that you (and your opinion and experiences) have nothing to do with what you're writing about.
Let's say I was writing a summary of the story of "The Three Little Pigs." (You know, the fairy tale / nursery rhyme where the Big Bad Wolf comes and huffs, and puffs, etc.)?
I would write something like, "This story tells the tale of three pigs who each choose to build their homes out of something different. The first pig builds a house of straw, the second a house of wood, and the third a house of brick. When a 'big bad' wolf came and threatens that he'll blow the pigs' houses down, only the house of the little pig with the house of bricks withstand the threat."
Do you see how the above summary doesn't involve the first person? It is simply a shorter retelling of the main points of the story. I hope that helps you!