I've been playing Amumu a lot lately, and I love him!
My only problem is when it comes to builds because I couldn't make a good build to save my life. I generally play Tank or Tank/Jungle Amumu. Although, I don't jungle a lot with him just because I'm not a fan on how reliant he is on blue buff, so I mainly lane with him. I'm following one guide I found online. I could only really find one that was a tanky build (there were some tanky AP builds, but I don't quite know if I should go with that or not).

Here's the items the guide says:
Regrowth Pendant + H. Pot -> Philo's Stone
Heart of Gold
Boots -> Merc Treads or Ninja Tabi
Sunfire Cape
Abyssal Scepter
Rylai's
F. Heart
FoN
--------------
Situational Items:
Athene's
B. Veil
G. Angel
Randuin's Omen
Shurelya's
Thornmail
WotA
Aegis of the Legion

I don't really know how I could improve this, and I don't know if I should consider the tanky AP build, so I need some advice. How should I improve this? And, if you do think the tanky AP build is the way to go, what items should I consider?
Thanks!

Oh, I forgot to mention. Are any of these situational items not recommended?

AP Amu is the ONLY Amumu build to go with; it makes the most use of his capabilities as a champion. Not making use of his AP scaling is generally a waste. He can deal a ton of damage with AP, which is why they recently nerfed some of his ratios (it's still effective however).

Shurelya's and Randuin's are definitely the standard items in that "situational" list because they build from the Philo Stone or HoG. Those are typical because Amumu is usually going to be your team's initiator (although the Support may buy these, but two Shurelya's on a team is entirely viable).

Athene's is a great item for Amumu, but it's especially helpful if you're being counterjungled (and just about any GOOD jungler will counterjungle Amumu's blues early-mid game). It basically allows you to get by without your blue buff.

I wouldn't recommend Aegis of the Legion on Amumu however. The support will almost always buy this, and even if they don't, it's not nearly as effective on Amumu. Amumu positions himself in the middle of the enemy team, pefect position to apply debuffs to the enemies. Aegis requires you to be in the middle of the ALLY team to apply the buffs (although the range is pretty large, so it's not entirely useless).

I love WoTA on Amumu. More of a late-game item for him really, but try it out when you get a chance. He can deal massive AOE damage in a fight with an AP-build. If you build Randuin's on him, you could probably replace Frozen Heart with WoTA.

making use of amumu's ap ratios is good for a lot of reasons. a favorite item of mine to buy would be abyssal scepter for those hard initiates. of course aegis isn't that good for amumu but building it out of habit is a style of mine. im usually the tank for my friends when we duo queue or do 5 man premade norms. no clue why nobody likes it. so much fun :3.. anyway amumu is a very ap heavy tank while building him flat ap is very viable (not as much now after the scaling nerfs) its not a recommended thing to do.
WoTA is nice imo but its not something that is necessary to tank efficiently. yeah hes dealing a lot of damage with q ulti e and the constant crying but i don't think the health you gain back from that will be noticeable shurelyas and randuins are definite necessities for any jungle tank imo. whether you buy the shurelyas or not is totally up to you cause i usually start boots 3 pot into HoG and just start building items based on the enemy teams comp. philo stone is amazing for amumu yes but idk why but i haven't gotten into the habit to sink another 800 gold into a second GP5. idk how cost efficient it is to sink 1600 into 2 GP5's but i don't like doing it.

my build for jungle amumu : boots 3 pots -> (after a successfull gank or 2) -> HoG -> Merc Treads -> Sunfire -> Abyssal Scepter -> randuins or shurelyas (depending on which GP5 you got) -> Rylais (nice health and ap) -> last item is situational cause its really team comp dependent Heavy physical damage team: go Thornmail heavy magic damage team: FoN

just my 2cents. i personally like aegis on amumu cause you can pull off a lot of dumb **** with it. and it makes you pretty tanky early on. later in the game you can sell it for another situational item but its really all based on experience. the more you play amumu the more you get used to a specific build that fits different team comps.

edit: oh yeah forgot to mention. NEVER BUY WRIGGLES. EVER. if your buying wriggles on amumu or skarner or any ap/ad tank champion chances are your gunna lose the game cause wriggles sets you back so much gold. remember amumu and skarner use skills more then they do auto attacking so wriggles is terrible on them (or any tank in particular)

Wow. That's a lot to remember. Mind you, it was helpful.
The thing is I don't understand how to make a good build and how impacting items are. Like some people say, "Don't go with Shurelya's." and others are like, "No no! Shurelya's is awesome!" In the end, I don't know whether or not I should go with it because people say different things and I don't even understand how Shurelya's works; I just go with what people tell me to! I don't know whether or not certain items are helping me or how items with low Armor, MR, or whatever are still beneficial even though it appears that its stats are low.
Anyways, if there were such things as LoL classes, I'd so be attending them. XD

I build amumu.

Boots w/ 3 mana pots
Build Rod of ages
Build Rylais
Build Rabadons
Build abyssal scepter
Lastly get banshee vail