Set in Academy City, a city of scientifically advanced superhuman students, located to the west of Tokyo, in a world where magic is also real. Kamijou Touma's right hand, the Imagine Breaker, can negate all magic, psychic, or divine powers, but not his own bad luck. One day he finds a young girl, Index, hanging on his balcony railing. She turns out to be a nun from the Church of England, and her mind has been implanted with the Index Librorum Prohibitorum — all the magical texts the Church has removed from circulation. His encounter leads him to meet others from the secret world of science and magic and right into an adventure where science and magic collide.

Touma's unusual power then places him at the centre of conflicts relating magicians and science-based espers in Academy City. As Touma tries to help and protect his friends, he learns the people he knows are not quite what they appear to be. To make thinks worse he begins to attract the unwanted attention of powerful magicians and espers alike, as they try to unravel the secrets of Academy City and Index.

[Source: AniDB]

Academy City is a highly developed place in terms of technology. It is said to be 20 to 30 years ahead of the rest of the world. Eighty percent of its 2.3 million residents are students. The focus of studies here is directed towards esper powers. Misaka Mikoto, one of the top level espers in town, shares a room with Kuroko Shirai, another high level esper who is a member of Judgement, a law enforcing agency composed of students. Both attend to Tokiwadai, a private school reserved for the high-leveled and the rich. Kuroko's partner at Judgement, Kazari Uiharu, is a low level esper who studies at Sakugawa middle school. Her best friend and classmate there is Ruiko Saten, a level zero (no esper powers). Together the four encounter several adventures in the exciting scientific town.

[Source: Anime News Network]

Shorts included in the first and fifth Blu-ray/DVD volumes.

Special beach episode bundled with the official visual book.

Continuing after the Level Upper incident, another phenomenon torments Misaka. A phenomenon called "Someone's Watching," its effect feels like the electricity in one's body flow backwards. With the help of her friends, Misaka fights against the unknown enemy.

[Source: MyAnimeList]

When science and sorcery clash, the result is explosive in this sequel to A Certain Magical Index from the studio that brought you Shakugan no Shana!

The Book of the Law—an encoded grimoire containing catastrophic magic—has been stolen, so naturally Kamijo, Index, and a few familiar faces join in the crusade to protect the one nun who can decipher the powerful text. But as the group battles church sects and holy assassins, they realize that discovering who their true enemy is may be more difficult than saving the sister. Meanwhile, an organization known as the Science Society resurrects an esper-producing program, a school festival brings out the competition—and drama—in the student population, and a mysterious figure negotiates the purchase of a sacred relic that could threaten the future of Academy City.

[Source: Funimation]

In the movie's story, just before the completion of the Academy City space elevator "Endymion", the main characters Kamijou and Index encounter a level 0 girl named Arisa. The Magicians are after Arisa, and they attack Academy City. A female leader named Shattoaura leads a unit from Academy City against the attack. Kamijou and Index learn from Stiyl that Arisa is key to a brewing war between the sides of Magic and Science.

[Source: Anime News Network]

The second season will focus on The Sisters Arc. Lasting only a single volume in the Toaru Majutsu no Index light novels, it was later expanded greatly in the Toaru Kagaku no Railgun manga.

The arc focuses on the ordeals of Mikoto Misaka after discovering the existence of the Radio Noise sisters that are being used in the Level 6 Shift, an experiment where they are killed in order for the highest-ranking Level 5, Accelerator, can achieve Level 6.

[Source: Wikipedia]

Shorts included in the Blu-ray/DVD volumes.

Blu-ray OVA bundled with the official visual book of Toaru Kagaku no Railgun S.

Science, magic, and a nun on the run! Kamijo and Index return just in time to celebrate A Certain Magical Index’s 10th anniversary with a brand-new season. After their deadly struggle against the Catholic Church and the pending war between magic and science, Kamijo must work harder to protect Index. But with tensions high all around, what new adventures await them in this next chapter?

[Source: FUNimation]

After rescuing Last Order and subsequently taking a bullet to the head, Academy City’s top-ranked esper rests in the hospital. But Accelerator’s recovery is cut short when a mysterious girl carrying a photo of his little clone companion asks for help. Now they’re taking on Disciplinary Action—an anti-evil coalition whose sinister plans threaten Last Order, Academy City, and even the entire world!

[Source: Crunchyroll]

Special included on the first Blu-ray/DVD volume of Toaru Kagaku no Accelerator.

Mikoto Misaka and her friends prepare for the Daihasei Festival, a seven-day athletic competition between esper schools. Academy City opens to the public for the event, but with the whole town abuzz, no one notices when trouble stirs behind the scenes.

[Source: Funimation]