Professor X and Magneto, in order
To watch Professor X and Magneto's story in order, start with X-Men: First Class, then X-Men: Days of Future Past and X-Men: Apocalypse. That's 8 out so far, about 17 hours, ending with Logan.
The friendship and rivalry between Charles Xavier and Erik Lehnsherr runs through the whole X-Men saga, played by James McAvoy and Michael Fassbender when young, and Patrick Stewart and Ian McKellen when old.
Updated
Professor X and Magneto's story in order
X-Men: First Class
Charles and Erik meet in 1962, and become enemies.
X-Men: Days of Future Past
The old and young Charles work together to change the future.
X-Men: Apocalypse
Erik loses everything again, and Apocalypse recruits him.
Dark Phoenix
Jean Grey's power tests Charles' leadership.
X-Men
Patrick Stewart and Ian McKellen take over the roles.
X2
Charles and Erik are forced to work together.
X-Men: The Last Stand
The Phoenix, and a cure for mutation.
Logan
Charles, very old and dangerous, in 2029.
Questions
What order should I watch Professor X and Magneto's story in?
Start with X-Men: First Class, then X-Men: Days of Future Past and X-Men: Apocalypse, and follow the list above: 8 in all, ending with Logan.
How long does it take to watch all of Professor X and Magneto's story?
About 17 hours for the 8 out so far.
Should I watch the X-Men prequels or the original trilogy first?
Either. Release order starts with X-Men (2000). Story order, used here, starts with First Class in 1962.
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