Core / root / foundation: Dark Seal + Liandry

There are two approaches to this, some Udyr players like to buy seal on their first recall, or even second, and there are other Udyr players that believe that delaying your Liandry by 350g is too much, and that you should buy it after.
Liandry and a 10 Stack dark seal will hard carry your damage, especially amped by liandry passive, and the ability to flex into Mejai at any point, you are also backed by Gathering storm as the game goes on.


Boots:

Say it with me:
"WE DO NOT BUY BOOTS FOR DEFENSIVE STATS, WE BUY THEM FOR THEIR EFFECT".
Ok, now we can proceed.

[*]If majority of enemy damage is coming from auto attacks, we'll be going steelcaps, this is actually majority of games that this is true.
[*] If enemy has champions that are GOING to land CC on you 100% and the duration is so long you will die during that CC, you must build mercs. (some crazy examples of this are: fiddle, leona,twisted fate) DO NOT BUILD MERCS VS KNOCKUPS,tenacity doesn't work.
[*] If enemy has MULTIPLE sources of slows (Zilean,Ashe,Rylais User or Lissandra) swifties value goes through the roof, unfortunately some games like that it's likely better to go mercs with DMP because of CC duration
[*] Lucidty / Ionian: If you're so snowballed by Liandry completion, if you know by 10-15 minutes the game is already over, you can win more, win faster with these.
[*] If for some reason you are SOLO AP, and you don't need defensive boots, you can consider going sorcs for a silly amount of damage, these games will be 1 in a million, so don't worry about it too much.

Armor items:

Frozen Heart: We CAN just do the Pentaless Nunu deluxe. Liandry -> Frozen Heart for the armor + CDR, haste is OP, and since Liandry doesn't give you haste, this makes having a Haste item 2nd very nice for spamming spells at our 2 item fight. He builds it every game regardless of the effect being useful on enemies (slowing their AS) the one downside of this item is that it doesn't contain HP. When you build this item, make sure you buy a ruby crystal afterwards, with the negatron from Kaenic.

Dead Mans Plate (DMP): Similar to Pentaless' Approach to Frozen heart being good regardless of the effect on enemies, you're able to just go DMP 2nd on Udyr regardless of the effect of slow resist. You can brain off go DMP 2nd everygame, and the movementspeed, and bonus frontloaded damage will feel good. Synergy with Celerity also feels nice.

Randuins Omen: Any time there are 2+ sources of crit on enemy team, the value of this item skyrockets (think of: GP top, Viego jg, Draven or cait ADC). I think this is the best armor item because it's 75 armor (the highest of all armor items and contains the most HP) It's also 200g cheaper than DMP (2700 vs 2900).


Magic Resistance Items:

Kaenic Rookern: THE premier MR item. 80 MR, you will legit take no damage, and negatron buy is so OP. 850g for 45 MR.

Force of Nature: 125 MR + a ton of MS when fully stacked, ONLY build this when enemy has built in DoT / Burn / Rot champions. Brand, Malzahar, Teemo, Swain, Mel. TThink of any liandry or blackfire torch user. One spell from them, and you're sure to have a fully stacked item that turns their damage to nothing.

Spirit Visage: ONLY build this when the following conditions are met: You have an insane HEAL+SHIELD support: Sona/Seraphine/Milio, especially with additional external shielding like a shen R in the same game, this item has insane value because you MUST be grouping and fighting near "Aura" allies (sona and seraphine have radius spells that hit everyone around them). Shit stats as a standalone item, and only shines when the conditions are met. DO NOT build this vs Akali,Leblanc,fizz or any real AP one shot threat, they will nuke you.


4th/5th item+

Mejais: Our best item, IF we play to protect our dark seal stacks, this item is so broken. It can be argued that this is a mandatory purchase every game.

Rabadons: If you don't have a 6-10 stack seal by now for some reason. Better than buying multiple defensive items, as your WW will be way more insane, as well as RR threat is going crazy, double synergy with gathering storm.

Riftmaker: If enemy team has multiple tanks that can't kill you, and the fights are dragging on very long. You can argue that Liandry + Rabadon synergy is simply better than Liandry+Riftmaker, I'm sure you can do the math on it or try vs target dummies with tanky items. This item is ALSO good to consider when you go frozen heart because it contains HP, and that's what's missing from frozen heart, so it's able to compliment it in the sense that makes up for what frozen heart lacks. Don't worry too much about the HP synergy that this item has, and enjoy the damage amp + Haste + HP.

Bloodletters Curse: If your team is very indexed into AP (3+)AND enemies are buying MR. AP black cleaver, easy to apply and good when those conditions are met.

Stormsurge: Always procs on your RR / QQ , 15 magic pen is good vs squishies, and so is the shock effect burst, 6% movespeed is nice as well

Horizon Focus: 125 AP for fat WW and a lot of damage increase on your phoenix+ A lot of Haste, good when your build lacks haste, reveal is a side random perk (funny to reveal khazix in his R)