It's the first series in the Nanoha franchise. Just considering anime, to date there's been:
Magical Girl Lyrical Nanoha (2004) (13 episodes)
Magical Girl Lyrical Nanoha A's (2005) (13 episodes)
Magical Girl Lyrical Nanoha StrikerS (2007) (26 episodes)
Magical Girl Lyrical Nanoha ViVid (2015) (12 episodes)
Magical Girl Lyrical Nanoha The MOVIE 1st (2010, alternate retelling of the 2004 series)
Magical Girl Lyrical Nanoha the Movie 2nd A's (2012, alternate retelling of the 2005 series)
What's unusual about Nanoha is its demographic. Magical girl shows are aimed at girls aged 6-11. They're superhero franchises where the heroine wears pink frilly dresses, hugs her friends a lot and has a magic wand. She'll have a cute animal sidekick and can be expected to defeat her enemies with love.
However magical girls shows have also been known to attract viewers like... well, for instance, me. Some of them are very good. Recently we've had deconstructive shows like Puella Magi Madoka Magica or Yuki Yuna is a Hero, but before them came Nanoha. Target audience: men aged 16-30. It's still a magical girl show, of course. However it's technically a spin-off of an adult computer game (Triangle Heart), the fights are serious and the "magic" has been realised as spaceships and gun parts. It's surprising that it's called magic at all. Nanoha's magic wand is like a souped-up version of Judge Dredd's Lawgiver. It verifies its user's orders in a mechanical computer voice and reconfigures itself.
This creates quite an interesting show... in theory. In practice, for a while it's pretty boring. It improves gradually and eventually gets good at the end, but that's still nowhere near a recommendation. I blame the underwritten characters.
We start with Nanoha Takamachi and a talking ferret who can turn her into a magical warrior. She has some friends, but she doesn't tell them about this. She doesn't tell anyone. It's just Nanoha and her ferret, called Yuuno. This goes on for three dull episodes. We're crying out for some more characters to get involved. Nanoha is well-meaning and serious-minded, but she's also one-dimensional and I never found her funny. Even her transformation sequence is oddly joyless and plodding, instead of being the explosive heart of what is fundamentally a superhero show.
Then a rival appears, called Fate Testarossa. This is an improvement, but unfortunately Fate is a woodenly stoic antagonist with the personality of toenail clippings. Is she good? Is she bad? I got no sense of life or motivation from her, although in fairness we do hear her say, "Wait for me, mother. I'll return to you soon." Nanoha and Fate's fight in ep.4 is empty, without passion.
Ep.5 is a hot springs episode, with fanservice. Hello, target audience! (It's pretty tame, though.)
The good news, though, is that the show's already started getting better. Fate is important, obviously, but she also has a passionate sidekick called Arf. The Time-Space Administration Bureau get involved, i.e. the multiverse police. Fate's mother shows up and she's absolutely horrific. Nanoha quickly realises that she doesn't want to fight Fate and keeps trying to befriend the other girl and get her to sit down and talk, even as laser cannons are getting unleashed.
The fights are decent, by the way. Both girls could be mistaken for natural disasters when really letting rip. They can shatter islands.
The good episode is ep.12. Fate's mother has delivered the bombshell to end all bombshells. You'd expect Fate's sanity to have shattered. Instead, she blossoms into a person, for the first time in the series. That had power.
Even at that late stage, though, I still have problems with the writing. Nanoha's friends and family get sidelined, which I wouldn't have minded so much if the show hadn't given them so much attention in the early episodes and made a story point out of Alisa getting upset about Nanoha keeping secrets from them. (How is this resolved? Answer: she never tells those secrets. Her friends never get let into the loop. There's an anti-moral to this story. At one point Nanoha says she told her mother "everything", but somehow she managed to do this without mentioning alternate universes, the supernatural or life-or-death battles. I can hardly imagine how she did this, although it doesn't seem likely to me that the resultant bowdlerisation could have contained much truth.)
Then there's the villain's downfall. When she died, I didn't realise she was meant to be dead. The post-mortem discussion in the following episode contained such a big plot trapdoor that I couldn't believe they weren't setting up her return. They weren't. That was it, unless she's coming back in one of the sequel series.
It's a weaker show than it should have been, I think. The characters aren't bringing it alive properly. Nanoha is a one-dimensional hero with no quirks, who doesn't generate comedy and doesn't even spend enough time with her friends. (Relationships can be a substitute for characterisation.) She's nice. I think she's a good person. However I think it's in large part her fault that the show isn't as good as its storyline. I see that other reviewers have also noticed that the show isn't as characterisation-based as most magical girl shows, instead focusing more on combat in a way you'd expect more from a Gundam mecha series. Is this deliberate, given the target demographic? Perhaps. That still doesn't make it a good thing, as far as I'm concerned.
I'm still curious about the 2010 movie, though. There are things I like here. It ends in a good place, with the cast having gone through enough for their further adventures to feel more meaningful. I like the way that the usual genre MacGuffin (here called Jewel Seeds) are as powerful as everyone says, as is underlined by multiple factions gunning for them. I like the irony of the friendship-focused Nanoha continually failing to make friends or to keep faith with the ones she has, whereas her enemies have bonds of absolute loyalty. (Sometimes to the point of stupidity.)
Hopefully the franchise improves. I've got my fingers crossed.