I am encountering runes a lot in campaigns, like protection runes at doors, but have not seen any source on how to create them. What is the source of such magic? Is it even possible to play a rune mage?
Paizo has no official concept of “rune magic,” rather both arcane and divine magics can create glyphs, runes, sigils, and symbols that have various effects. For some examples,
Sorcerers and wizards, as well as anyone with the rune domain, can cast the explosive runes spell, which creates runes that, well, explode when read.
Clerics, inquisitors, oracles, and witches can cast the glyph of warding spell, which harms those who attempt to bypass it.
Clerics, oracles, sorcerers, witches, and wizards can cast the symbol of death spell, which kills those who are too close to it when it is triggered (typically by looking at it, reading it, touching it, or passing over or under it).
The rune domain includes many of these sorts of spells, and would be quite fitting for a character who is supposed to be particularly interested in runic magic. But ultimately, that character would just be a regular spellcaster who favors certain spells that share a theme, not someone who uses a special or unique type of magic.
For a more unusual sort of rune, there are the sin runes, which are basically a special sort of magic item, of which a character can have only one and can activate it with a command word as a standard action. They can be created using the Inscribe Rune item-creation feat, which is available to any spellcaster with caster level 3rd, but the prices of the runes are much too high to consider for a character of that level (the cheapest, by a lot, are the rune of the inscrutable one, at 36,000 gp and the rune of resistance at 45,000 gp; the next cheapest is the rune of razing at 91,000 gp and the rest are all above 100,000 gp). Thus, Inscribe Rune is probably only worth considering at quite high levels, and only if a couple of people in the party would otherwise pay full price for a sin rune.
Finally, third-party book Ultimate Psionics includes a variant on page 142 for treating their psionics rules as rune magic, by simply renaming things. It’s a rather interesting take that I enjoy much more than the above.
There are a variety of rune based spells in pathfinder. I'll list a few (though this is not a fully comprehensive list).
- Glyph of Warding
- Fiery Runes
- Arcane Mark (particularly with Instant Summons)
- All the Symbol Spells (i.e. Symbol of Death)
There is also a cleric domain called Rune Domain that will let you create "blast runes" and at 8th level let you attach other spells to your blast runes.
Additionally (though this does not create an actual rune but does make a magical trap) there is a Word (from the UM wordcasting system) that will allow you to attach word effects to someone else opening an object called Lock Ward