Aesir Monument
The Aeisr Monument is unlocked while progressing through the main story shortly after you finish your T2 job advancement. Once you progress through the main story enough you'll have a green quest called "Aesir Monument". Head to Prontera to the Aesir Monument Valkyrie named Orloum. Talk to this NPC to receive the Aesir Monument and some contribution & gold medals.
Location of the Aesir Monument NPC
Aesir Monument
To access the monument use it from your inventory.
Some of you may recognize this as the Sphere Grid from Final Fantasy 10. This follows the same concept, allowing you to spend contribution and gold medals to unlocking nodes along the path that grant stats, boost existing abilities, and even give you brand new skills.
These nodes are unlocked by spending contribution and gold medals. Most nodes only need contribution but there are special nodes indicated by a flame icon that contain special things such as new skills or changes to skills. In the example above the Lunatic Gunnver IV skill grants me a new skill and costs 30 Gold Medals and 4500 contribution. Both of these resources are primarily obtained from the guild donation NPC but gold medals always require MINI or MVP material drops such as four leaf clovers, star crumbs, etc.
If you notice at the top of the screen there are two sets of icons for contribution and gold medals. The ones on the left with no lock icon are in your inventory and have never been spend in the Aesir. Once you spend them they are converted to locked currency like shown at the top center.
All gold medals and contribution become locked to that character. However, you can be use all of them on each multijob, they are not split! To be absolutely clear, this means that if you have 1000 gold medals then you can use all 1000 on knight, then multijob to wizard and use alll 1000 again. You don't have to get them separately for each class giving great value to multijob.
Here is a link to a planner tool so you can see what options are available for your class: https://www.romcodex.com/runes/
Finding Nodes
At first you'll have to look through your Aesir to figure out which node(s) you want to head for but once you're familiar with the name of the node then you can always look it up using the Search box. Click the dropdown in the search box and select the node to find and it will highlight in the minimap at the top right of the screen. If you head over to where that node is it will glow so that it stands out on your screen.
Clicking the dropdown to search for a node
What the nodes look like after selecting a node to search for
You can also view the values of stat nodes at a glance by clicking the button at the bottom left that looks like a hexagon with a slash through it.
Location of the View Stat Values Icon (Bottom Left)
Zoomed in to see Stat Values better
Pathfinding
While you can assign points one by one you can also tap on the node you want and it will find a path to that node based on your current progress through the monument. There are two pathfinding algorithms used for this:
Shortest Path: Finds the quickest way there
Fewest Medals: Finds the quickest way there while consuming the least amount of Gold Medals
I've provided examples below showing both algorithms in action for a node I'd like to reach. The fastest way there costs 90 gold medals compared to the fewest medals path which only needs 40.
Fewest Medals Path which only needs 40 Gold Medals
Shorted Path which needs 90 Gold Medals
There is also a path planner tool at the bottom left that you can toggle on and off. After selecting a node to path to and clicking the activate button you can click the green Default button which will save that path. You can toggle visibility of this path by clicking the path icon at the bottom left which highlights a yellow path to the selected node. You can add more paths and add those too and these settings persist so you can plan out paths to your next few nodes and quickly follow your chosen path.
Location of the View Path button (bottom left) and Reset to Default which adds it
What the screen looks like when View Path is on
Forewarning, I could not for the life of me figure out how to clear the saved path out so this may not work as intended...
Comparing
After selecting a path you can see exactly how many stat increases you're getting along that path by clicking the blue Compare button at the bottom right. The screen that pops up shows your current investment into the Aesir as well as the new attributes that you're planning to add along the selected path.
Path to compare
Stats gained (on the right) for adding this path
Resetting Points
You can reset your nodes anytime by tapping a node to remove and selecting the yellow Reset button at the bottom. This will show you how many points will be reset and the zeny cost (if any) to do so.
Clicking on the Center node and clicking Reset
What it looks like after you click Reset
To confirm click the Blue Circle at the bottom, or the red X to cancel.
Quick Allocation
If you reach a point where you've gotten all the nodes you need and just want to throw your resources into the Aesir wherever there is a Quick Point Allocation button at the top right that will allow you to do just that. This is more useful for people who have maxed out their Aesir so you can quickly allocate everything when you multijob a new class.
Layout and Expansions
The layout of the Aesir Monument is identical from class to class except the contents of the nodes change based on the class. A spot where you unlock a new skill for Priest may simply be a buff to a poison skill for Assassin. Familiarize yourself with your Aesir and figure out which nodes to go for first, primarily focused on buffs towards your primary source of damage.
As you progress further into the game you'll have opportunities to expand your Aesir to grow out further, offering you new abilities, buffs, and more buffs your older skills. Even a base job skill like Bash from swordsmen gets a few more damage nodes at third job so keep an eye out when you expand, you may find new enhancements to existing abilities.
Layout of the initial Aesir Monument
First Aesir Monument Expansion Unlocked at Second Job (Green is New)
Second Aesir Monument Expansion Unlocked at Third Job (Green Area is New)
Final Aesir Monument Upgrade at Third Job Lv40 (Green Shaded Area is New)