And I thought "precision clicking" was a joke... 6-link in 6 fusing
I can die in pieces now...    

General Concept
There's 16 tiers of general maps. T1-T5 = white, T6-T10 = yellow, T11-T16 = red.
When you open your atlas for the first time, you can only see 4, at each corner, that's T1.
When you do a map, there is a possibility the next tier neighbor map will drop, which is shown with the dotted lines linked around.
Basically we call this "progression", we want to progress to the next tier, next next tier, and so on.
Let say you do Dungeon, Flooded Mine will possibly drop. If you do Flooded Mine, there's 3 possibilities for T3 - Excavation, Leyline, Cells. So on and so forth.

When the map is completed (kill the boss), it is now available to drop from "globally" (anywhere), instead of tied to these links.
But next tier drop is not guaranteed, it's not uncommon to get shitty T1 when you do T15 maps even...

Map Crafting
You craft map just like crafting equipment, using those various orbs.
For casual like me, I just slam an Orb of Alchemy on it, as long as it don't have scary mods then I just run it and call it a day.
For more serious people, they enhance stuff with "Sextant" (adding more mods through Atlas), slamming chaos until they get high "Pack Size" (monster density), increase map quality by using "Chisel", and also increase quantity further by adding "sacrifice fragments", and then there's "sextant blocks", blah blah blah...     

Because orb of Alchemy is frequently used to craft map, that's why we often sell junk unique loots by 1 alchemy.
If I don't like the mods, I can either use Scouring Orb then slam another Alchemy again, or just use Chaos Orb to re-roll.
The last boss of Atlas is Shaper (T17), which you can do after you get 4 map fragments keys from each T16 map boss.

Tentacle VS Galaxy
The "War of the Atlas" is a whole different story added in this current expansion.
You got Elder (tentacle) and Shaper (galaxy) randomly spawn on Atlas.
If you complete a Shaper influenced map, either by killing the map boss, or kill >60% of monster - this map will no longer have Shaper influence.
If there's a tentacle at adjacent of the map you completed above, the tentacle will take over.
This is how you push shaper/elder around the atlas.

Ideally, what you want to do is to get as much Elder (tentacle) influence as possible, because there two things you can only gain by having maps under Elder control:
- get memory fragment from certain map boss (will highlight with blue circle), this is for quest to get "Shaper's Orb".
- trigger Elder boss fight when there's enough linked map under Elder control in a cluster

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Shaper's Orb
Shaper's Orb comes in various tiers, you use this orb to increase the tier of a map by 5.
Let say I loves the map "Excavation" which is a T3, but it's no longer good to do when you already very high level.
I will use "Shaper's Orb T3", to convert Excavations into a T8 map, making it better for high level.

Uber Labyrinth
- Just like Merciless Lab, this unlock the final 2 points to spent on your ascendancy
- you encounter trials (total 6 types) when you doing maps
- after you completed each trial and click on the "board" thing, remember to pickup the "Offering to the Goddess", that's they key to Uber Lab after you completed all trials

Misc tips:
- you want to complete maps' bonus objective for every map, it's only a one time deal for every map
- vendor 3 same maps you will get one next tier map
- vendor : Stone Hammer / Rock Breaker / Gavel of QUALITY 20% + a map = one Chisel .... ideally you just use white weapons, cuz it only require 4 Wheatstone to get to 20%.
- even if you don't want to use CHisel yourself, you can amass it for trading purpose
- because you only get 6 portals each map, don't pickup all the shit you find, use a good loot-filter.
- there's also "capture boss soul" thing that tied to the "Pantheon" stuff, you need am item "Divine Vessel" to capture boss soul but it's kinda rare drop
- the challenge "complete map with 8 mods", only corrupted map with Vaal Orb can have up to 8 mods or more, there are various single mods that appear as multiple lines.
- invite Zana to your hideout (home) as soon as possible to get her map machine, so you don't need to run to that prologue area anymore.
- maps opened by Zana mission do not count towards Atlas, unfortunately
- level up Zana to unlock more options on her machine
- after completing map bonus objective, the boss is kinda become mostly optional. Not that it guarantee high tier map drop anyway, sometime it just not worth the risk - levelling after 85 gets a bit slower, dying is terrible.

Other resources
If you don't understand something just hit the POE Wiki.
Also good to check out some youtube channel like Tarke Cat's. He got some video recently about atlas progression, sextant and stuff.
https://www.youtube.com/channel/UChvPdtXbl0nJNqo3wF39sqg