I'm watching the 3rd season of the anime, and after that, I would like to continue with a version of the story which tells more events or situations or details which werent told in the anime. Which version of A certain magical index is more expanded, the manga or the light novels?
The Index light novels are the source material, so the light novels are the most expanded. The Index manga and the Index anime are adaptations of the light novels.
Though to make things more confusing, there's also A Certain Scientific Railgun and A Certain Scientific Accelerator, which are manga spinoffs of the Index light novels. They have their own separate storylines, so the manga versions of these series are the most expanded for their respective storylines.
But to make things even more confusing, Railgun has a number of anime-original arcs that are not in the manga, but are acknowledged and back-referenced by the manga in later story arcs. But the Railgun anime and manga also have a number of timeline inconsistencies (e.g. the timing of Kongou Mitsuko's appearance). Oof.
The graph of Toaru adaptation relationships looks roughly something like this. In my diagram below, titles branching to the right are direct adaptations, and titles branching downwards are spinoffs. The year in parentheses is the date of first release.
Index novels (2004) ─┬── Index manga (2007) │ └── Index anime (2008) ├─── Railgun manga (2007) ──── Railgun anime (2009) │ └─── Astral Buddy manga (2017) └─── Accelerator manga (2013) ──── Accelerator anime (2019)
This is just a broad overview; there are also things like side-story light novels and games and movies.
For the Index anime in particular:
- Index adapts volumes 1-6 of the light novels.
- Index II adapts volumes 7-13 of the light novels.
- Index III adapts volumes 14-22 of the light novels.
That adapts up to the end of the original LN series, but there are something like another 22 light novels after that, under the sequel title Shinyaku Toaru Majutsu no Index (a.k.a. New Testament). See this list of light novels.
It also may be worth rereading the arcs that the anime covered, because the anime left a lot out (note that it had to compress 9 volumes of content into only 26 episodes). In the r/anime threads for Index III, Razorhead's "Small Facts" comment series on each episode details the differences between the anime and light novel, and clarifies a lot of details that may have been unclear due to omitted content. And some of these are quite lengthy. (Some examples: episodes 1, 2, 3, 4, 5, 6)
See also Baka-Tsuki's Index Calendar. It's a bit out of date at the moment, but it's a good overview of where all the various light novel, manga, and anime adaptations in the Toaru Verse are currently up to in-universe, timeline-wise.