It's a softer, gentler spin-off of INDEX, sidelining almost all of the parent show's main cast to focus on different people instead. Touma occasionally appears, but this is mostly the story of 14-year-old Mikoto Misaka and her school friends. They hang out and go to cafes. They watch fireworks. They get scolded by their school dorm mistress for staying out late.
However some of them also have superpowers. They'll defeat villains, although infrequently enough that you could forget that Misaka's the third strongest psychic in Academy City. There are two serious dramatic story arcs, one halfway through and the other at the end, but they're rarer than and unlike the parent show's. Magicians never get involved. Everything's more down-to-earth and scientific, as well as being something of a cop show. In a world where teenage psychics can be more powerful than SWAT teams, you can see how they'd get recruited into law enforcement agencies. There are two such agencies: Judgement (who seem more like detectives) and Anti-Skill (who seem more like coppers on the beat, or sometimes troops). It's definitely not a hard-boiled cop show, though, and these teenage police officers are capable of making sentimental errors of judgement that will make you want to throw things at the screen.
Is it a good show? Yes, up to a point. As with INDEX, I enjoyed it and merrily ploughed through lots of it at speed without thinking it was anything special. It's decent anime. It's basically okay and likeable, but it's not one of the top-drawer shows you'd push as a gateway drug for newbies.
The main cast are:
1. MIKOTO MISAKA: likes frogs and childish things, about which she's a bit embarrassed. A bit of a tomboy. She can also control electrical and magnetic fields, to a degree that can turn a flipped penny into an anti-aircraft missile. Her pennies only have a fifty-metre range because after that, they vapourise.
2. KUROKO SHIRAI: a love-or-hate character, whom as it happens I love. The controversial bit is that she's a lesbian molester who's in love with Misaka and has to be watched like a hawk to make sure she doesn't become an outright sex offender. She also talks like a granny, is prone to eccentric ideas and is the show's biggest loon. However she's also a highly effective member of Judgement, with excellent cop skills, a high level of professionalism and a superpower rank only one level below Misaka's. She's a teleporter. Break the law in her presence and she'll nail your clothes to the pavement with steel rods.
3. RUIKO SATEN: an ordinary schoolgirl with no powers. (This makes her the odd one out and she's got a slight complex about that.) Also prone to mild sexual harassment of her best friend, although at a far, far lower level than Shirai. You might be spotting a trend.
4. KAZARI UIHARU: kind, modest, mild-mannered. Has the brains of a flower meadow in the last story arc and personally I'd have sacked her from her job with Judgement. Useless in combat and has such a low-key superpower that her friends don't even know what it is, but she's great with computers.
The burning question, of course, is "What's the correct watching order?" This show happens in the background of INDEX and the two shows' timelines intertwine, so it's not clear how one should attack it. Most people say "broadcast order" and that's what I'm doing, but strict chronological order would go like this:
RAILGUN eps.1-14 + OVA (Level Upper Arc)
INDEX eps.1-6 (Index Arc)
RAILGUN eps.15-16 (Big Spider Arc)
INDEX eps.7-9 (Deep Blood Arc)
RAILGUN eps.17-24 (Poltergeist Arc)
...and that's still barely a third of the way through INDEX season 1. If you were wondering about the Sisters arc and other Misaka-heavy INDEX episodes, they're in RAILGUN season 2. This first season isn't retelling any stories we've seen before.
It's an amusing show. It made me laugh. It can feel a bit like filler, partly because it sort of is, but it also can get emotional when it steps up for a serious story arc. (Ep.18 is another favourite of mine, partly for how many different things it's doing in twenty minutes.) Also, apparently the RAILGUN anime outsold INDEX and was better received by a lot of fans. (That's the anime rather than the novels, mind you.) It's a light novel adaptation without the wish-fulfilment male light novel protagonist, instead having an almost all-female cast. It's good, solid second-tier stuff. Don't drop everything to watch this, but it's entertaining enough.