How to increase mana regen?

Your first option to boost mana generation is in Sovereign Creation.  Attunement produces an additonal 2 mana per turn.

Building on Shards also increases your mana regeneration, by the number of elemental shards you control.

There is a technology (Greater Shards?), that increases the mana generated by the Shards.

I believe there are some arcane buildings that also increase the mana regeneration rate.

As for Enchantments, it looks like you can have up to your Mana Generation rate in Enchantment upkeep costs.  I don't know if you are allowed to go over (and deplete your mana pool by the excess every turn), as I haven't tried to exceed that rate yet...

That's all I've seen so far in 1.09p.

I think now, Sovereigns generate 2 mana per turn (or 4 with Attunement), Shards controlled generate 2 mana per turn (as of 1.09o), and Greater Mana Shrines generate 3 mana per turn.  And AFAIK, you can have a negative mana generation rate, where you will actually lose mana per turn.  And I would think, given that Heavenfall's Faction mod allows the Goblins to start with negative mana, you would go into negative mana eventually, which would have the effect of preventing any new spell-casting until you have at least a positive amount of a particular spell's cost.  Not sure if spells requiring maintenance would be automatically cancelled if you had negative mana (but my (complete guess) would be no).

Best regards,
Steven.

You needed more mana regen? I got a bug that generated around 200 mana in the first few turns in a epic setting.

Summon familiar and arcane weapon are very cheap to cast, and for a reason. Cast them for 1 mana, and dispell them when you don't need them. Save your mana! There dosent seem to be too much of a limit to how much you can cast from the overland map, I quite often find my self casting  weapon on all units before  a battle then dispelling it after if their is no combat straight up.