In a place called Mikitahara(I think that was its name?), There lived a girl named Madoka Kaname, who had an
oblivious sheltered life. She had strange premonition dreams about a tall short dark haired bishoujo girl fighting a monster. Then the next day a girl named homuhomu Homura Akemi, who looks exactly like the person in her dreams, shows up and transfers to the school.
After school, Madoka hears a voice calling her
to her doom for help. She naturally decides to check it out and finds an alien weasel-like thing that can talk to her mentally. Homura shows herself and planned to kill that thing when suddenly, Sayaka Miki, Madoka's best friend, also shows up and blasts foams Homura to save Madoka and that thing. As they escape, they are brought in a strange world where there are deadly cottonballs with scisors. They then are again saved by a girl who is a Puella Magi(magical girl) named Mami Tomoe, who has unlimited flintlock works plenty of rifles that wipes out all the fluffy cotton. After healing the strange thing, it finally says that its name is incubator Kyubey who will grant your wishes if you decide to sign a soul contract become a Puella Magi.
Oh and then later another Puella Magi shows up. Her name is Kyouko Sakura and she likes to
tease provoke Sayaka, who eventually becomes a witch Puella Magi. She then later develops an obsession soft side to Sayaka.
The world of Madokaverse is pretty strong. Magical girls have abilities that range from being able to create an unlimited(?) amount of guns/swords, spears that can grow to gigantic levels, time magic that can stop and rewind, arrows that can destroy universes, etc.