As the title states, this is not a full guide, mostly just a build with a few explanations to go along with it. So lets get started.

NOTES ABOUT STATS AT TOP: The stats at the top do not take into account anything other than the flat bonuses from the items and runes. This means that the masteries are not represented as well as the 30% increase in AP from Deathcap. Below is the actual stats at level 18 with full build

The MrP (Magic Penetration) Marks are used because Elise's main damage dealing spell is Neurotoxin/Venomous Bite which has a pretty low AP ration. It mostly does its damage through percentages and percent based damage works better with MrP.

Armor Seals are for jungling early on when runes are most effective.

MR/lvl Glyphs for better resistances for when you hit level 18 and need a bit more survivability late game.

I prefer MS Quints as they work equally well for any champion. But on Elise it allows you toget that tiny bit of extra speed to catch or run away if you have already burned your rappel. Other options include AP or ArP Quints.

EDIT: If you change MS Quints to AP Quints, it gives you 401 AP by end of build. This means another 2 full % on your Q damage. Might be for some people, might not, I still prefer the extra speed.

For masteries I went with a 9/9/12 setup. I chose this for the same reasons as with runes:
Offensive:
I want to focus on MrP over straight AP. The cooldown reduction also helps.
Defensive:
Pretty self explanatory, armor for early jungle, health for that added kick and MR for...well its too small to be a difference but its there.
Utility:
Summoner spell mastery for flash cd reduction. Max Mana and Mana regen masteries for Elise's human form spells. MS for same reason as Quints. Buff duration for maintaining buff control.

And for the part everyone probably skipped to: Items.
This item list is more for fighting teams that are pretty well organized and balanced where you will need MR and Armor, MrP for tanks and tenacity for CC. Obviously you won't always need all these items. This is just one of many possible builds and I shouldn't be the first to tell you that you should not follow this religiously. Also, being a jungler means you will not be getting the gold that your laners will be getting, keeping this in mind i try to keep the build relatively cheap, for early-mid game. Now to explanations:

Mercenary Treads mainly for the tenacity. The added MR helps a bit as well.
-
I went with a Shurelya's Reverie for 2 main reasons. 1) it builds from a philosopher stone which can help you with gold throughout the game. 2) The active MS boost on it will really help you out in ganks. The cd reduction and bonus Health are also very nice on her.
-
I went with an Aegis of the Legion as it is a very cheap but effective tanky item. it allows you to initiate with rappel onto their carry and (hopefully) survive to tell about it. If the game drags on for too long and you have already finished your build, I recommend trading this in for a Guardians Angel for even more survivability.
-
Void staff is an exceptional item on Elise as it synergies with her Neurotoxin/Venomous Bite very well. As i stated earlier, MrP works best with her Q due to lower AP ration but high % damage.
-
Rylai's Crystal Scepter is another great item on Elise, it gives a good amount of health to survive while in Spider form. The main reason for picking this up, however, is its slow. This adds a much needed form of CC to Elise to catch her prey without having to resort to Rappel.
-
Lastly we have Rabadon's Deathcap. This is an essential item on just about any major AP damage dealer.

TLDR: I wanted a mix of survivability to be able to land on enemies with rappel and not get bursted in a team fight, and damage output to actually get a kill. I also wanted to keep the build cheap as junglers don't get as much gold as laners.

The total cost of items in this build is 14324 Gold. You should be able to reach a full build by late game if you get some kills and Dragon a few times (which you should be doing anyways as a jungler).

Well that's about it. I know it's not very in depth or informational. I just wanted to post it to show people how I use her and maybe hear some feedback on things to add/change. Any and all comments are welcome. If you comment saying "This is trash!! Why would you even do this you [insert derogatory term here]." you will be ignored. it doesn't hurt my feelings or make you seem any "cooler" so whatever have fun. And to everyone else, thanks for reading (first guide/build btw!! :D) hope you enjoy. If I get enough comments/votes I may turn this into a full guide with pretty pictures and all.