Ulysses is the Roman name for the Greek hero Odysseus — the clever king in the old stories who fought at Troy and then spent ten years trying to sail home to his wife and son. Same man, two names: the Greeks called him Odysseus, the Romans called him Ulysses, and English took both. Which one you meet depends on which book you are reading. Older English writers (Shakespeare, Tennyson) say Ulysses; modern translations of Homer usually say Odysseus. If a student says "Ulysses and Odysseus are two different heroes", that is a very common mistake — they are one person. He is famous not for being strong but for being smart and tricky. The wooden horse at Troy was his idea. So when English speakers call someone "a Ulysses", they mean someone clever who talks their way out of trouble, though this is quite bookish and you will not hear it in daily conversation. Two other uses you may meet: Ulysses is also the title of a very famous, very difficult novel by James Joyce (1922), set in one single day in Dublin — people mention it as the classic example of a book everyone owns but nobody finishes. And Ulysses S. Grant was an American general and later president, whose face is on the fifty-dollar bill.