Inventory space in The Elder Scrolls Online, just as in any MMORPG, is one of the most important things to have in the game. Even more so if you are someone who likes to loot every single barrel, crate, sack, backpack, chest, dresser, cabinet, night stand.... I may have a touch of cleptomania when it comes to TESO, actually. 

For me, there is no such thing as too many bag slots, and I'm sure you're here because the same can be said for you. So, here's is a guide on how to get as much pack space as possible.

Buy Bigger Bags
This is an old stand-by... just go buy bigger bags! There are bag vendors and pack merchants in all major cities (and some less major ones too). You can find them on your map mixed in with other vendors. Look for the bag symbol next to their name, as in the picture to the right next to Quaranon.

Not all locations where you can buy bags are clearly marked with signage... sometimes it's just a cart, but often you can find a bag vendor by a sign posted outside their shop, like pictured to the right.

The only drawback to buying pack space is that it gets expensive quickly! Here's a list of the prices for purchasing bag space as you go, as of the time of this writing:
400 g
2000 g
5900 g
11000 g
19200 g

Each price level opens you an additional 10 inventory slots.

Buy a Horse, of Course
The next way to increase bag space is to buy a draft horse. Be warned, they're expensive at lower levels, but once you can afford it they are worth every piece of gold (all 42700 of them).

You see, as long as you have a pack horse in the stable, the amount of carrying capacity that it has is added to your available inventory space.

The initial amount of additional bag space this will net you is just 10 slots, but, you can increase this amount by feeding your horse Oats every day. Doing this will get you an extra slot in your inventory every day, until you have it maxed out at 49 feedings. It only costs 250 g to feed your horse, and it can be done every 20 hours.

Note, you can add additional carrying capacity to any mount, but it makes most sense to do it with a draft horse, as they have 10 more bag spaces than any other type of mount.

Bank Storage
Just as with your pack space, you also start with 60 slots of bank space which can be expanded for a fee... a much higher fee than that of your back pack. The first two tiers of upgrades cost:
1000 g
3300 g
...

As with bag space, each tier nets your an additional 10 slots of space.Bank space is shared between your characters too, so there is only so much value to having mules... but speaking of mules.

Mules / Alts
An old trick in MMOs is to create additional characters that you use only for storing your excess inventory in, and that works in The Elder Scrolls Online too. Just create a character, skip the tutorial zone and log it out in the nearest bank. Use the 60 slots that each character gets for putting in all the mats you don't need ready access to.

The Mail System
If you have a friend that you trust, you can also take advantage of how the mail system in TESO works. Just send them a message and attach as much stuff as possible to it, then have them return the message to you. You can just let it sit in your mailbox for 30 days, then rinse and repeat.

Don't forget about it though, as the message will be automatically deleted after sitting in your mailbox for 30 days!