I gonna talk about most of Catacombs Lore here, which I gonna use for the UT: Mod I'm currently doing.

The Catacombs is a location next to the Ruins, which was created to be a resting place to monsters which died during the War against Humans and Monsters.

The place can be accessed via a hidden room on the First puzzle room on Ruins. After asking to Toriel about leaving the Ruins.

The Catacombs looks like New Home by the gray color of the walls, but with a difference of having brown leave bushes around and having more cracks elsewhere. The Catacombs also have several puzzles (most of them being of pushing rocks).

While exploring this place, you gonna meet up with this Goat-monster called "Muchiel".

Muchiel, is the Guardian of Catacombs, and the Graveyard Keeper there too, also, Muchiel is the father of Toriel, (and by extension, the grandfather of Asriel.) Muchiel often morns about Asriel death (Reminder: He mentions this in a indirect way.)

While exploring there, you gonna find certain relevant NPCs, such as "Butterandra", a Butterfly-monster from another area of the Underground which owns a Bake Sale (and is also a rival of Muffet.)

But, while you explore even more. You gonna find these two ghosts.

These ghosts, are the ghosts which possess the two dummies which appears on Undertale, the Yellow one being the Mad Dummy ghost, and the Green one being the Ruins Dummy ghost.

There the "Mourning Ghost" gonna tell to "Mad Ghost" about what the Player/Frisk did to them. (the Dialogue might can change if the player had killed or spared the dummy.)

And the "Mad Ghost" would try get revenge from what you with their cousin.

Until you finally meet with them and being chased in a room which you need solve puzzles to survive.

But in the end while crossing a bridge, the Mad Ghost ends up cutting the bridge, making you falling down.

After the fall, you gonna get to the Catacombs Sewer System.

Where you gonna fight against Mad Ghost, until Muchiel protects you.

And after leaving the Sewers, you gonna get to the Catacombs Main Hub, and going north, and climbing long stairs, you gonna get into the Catacombs Graveyard. Where you gonna fight against Muchiel.

But then near the end of the fight, Toriel ends up interupting it, asking what her father is doing, but after some quick discussion, they ended up solving everything in the end. Then Toriel returns to her home in the Ruins, while Muchiel to his home on Catacombs. (Which can be accessed West of the Catacombs Hub).

And after that fight, you can go to the West to return to the Ruins, and then fight against Toriel.

Then ending the Catacombs storyline.