I am more of a PvE player and wonder how the dungeons and instances will work.

Will agro exist or will mobs attack at random

Yes there is aggro in the game. It doesn't work like it does in a game like WoW.

So how does it work?

From what I understand I believe aggro is obtained by stunning and interrupting as well as damaging and healing. The tanks that stun and interrupt will get most aggro and it's up to the dps and healers to use their skills selectively as to not pull aggro. It's also important to note that the enemy npcs are "smart". So if you're a range damage dealer the enemy archers and mages will focus you more. If you're a melee user warrior npcs and berserkers will primarily focus you. I'm not sure if there are any taunts in the game or AoE taunts that tank style players can use. But they can take and keep aggro with their interrupts and stuns on a single target like a boss or something.

To add on to this, the tanks are not meant to keep aggro on all the mobs in the group. They are to take on a couple to several, while the rest of the group handles the left overs.

If you're in a large room full of enemies don't expect to be able to pull them one pack at a time; they'll all jump in. As a result expect aggroing mobs that patrol hallways and the like to attack you on sight just like the mobs like the draugr do in Nordic tombs in Skyrim.

yes thanks for elaborating on that

From what I have read and watched in interviews what happens when you enter a room and alert the mobs that you are there, not just the ones who saw you enter come to fight you. All of the mobs come because the other mobs who did see you tell them to come join the fight. You can not stand there just out of agro range and beat down mobs while the mobs just out of agro range are oblivious to you and your group killing their buddies.

I personally really like that because I have always hated in MMO's where you can pull one maybe two mobs at a time and the others stand there waiting to be pulled. It is unrealistic and I think Zenimax saw it that way as well and decided to try something different.

Also when mobs fight you they will use skills in synergy with each other, just like players can.

However there are taunt abilities.

I must say that I'll be rather dissapointed if the A.I. is just a dressed up aggro system.

There shouldn't be, not unless they work in PvP. Imo. taunt shouldn't be in the game if they don't work on a human opponent.

But there are. Some abilities are just more usefull in PvE and some are better for PvP.
The 1 taunt (they mentioned that there are 2) ability which I know also reduces the dmg done by the target.

I hate to be the one to say it, but that's way too much like WoW. Taunt's is a detriment to what they're trying achieve with PvE in ESO. They don't want us to fall into the holy trinity system, well if they give tanks a taunt, then they can be sure we'll fall into the whole "Tank, DPS and Healer". Imo. they need to remove all abilities that don't work on other players as well. If there's a taunt that works in PvP, then that's fine. I just think we should be handling the situation where the mage is being attacked differently that they do in WoW. They simply taunt. It's unimaginative.

They have never said they didn't want the trinity in the game. They have said they don't want you forced into it, and you are not.