Olaf
My Axe is Thirsty
Lane harassment and consistent damage output.
Sorcery
Empowered abilities and resource manipulation
Arcane CometDamaging a champion with an ability hurls a damaging comet at their location.
Manaflow BandHitting an enemy champion with an ability permanently increases your maximum mana by 25, up to 250 mana.
After reaching 250 bonus mana, restore 1% of your missing mana every 5 seconds.
TranscendenceGain bonuses upon reaching the following levels:
Level 5: +5Ability Haste
Level 8: +5Ability Haste
Level 11: On Champion takedown, reduce the remaining cooldown of basic abilities by 20%.
ScorchYour first damaging ability hit every 10s burns champions.
Resolve
Durability and crowd control
Bone PlatingAfter taking damage from an enemy champion, the next 3 spells or attacks you receive from them deal 30-60 (based on level) less damage.
Duration: 1.5s
Cooldown: 55s
OvergrowthGain permanent max health when minions or monsters die near you.
Adaptive Force
+9
Adaptive Force Adaptive Force
+9
Adaptive Force 
Health Scaling
+10-180 Health (based on level)
Why Arcane Comet
Olaf's reliable slow with [W] makes your comet a consistent form of sustained poke damage during the laning phase.
Why Manaflow Band
Olaf can have issues with mana when spamming [Q] for poke damage so Manaflow Band helps you keep that up.
Why Transcendence
Mid game CDR on Olaf is huge for ramping your damage output with [Q] and [E].
Why Scorch
Scorch doubles down on you laning phase [Q] poke allows you to dominate lane with constant harass.
WhyBone Plating
Bone Plating's early game damage mitigation further pushes your dueling pressure in the laning phase to snowball a lead.
WhyOvergrowth
Overgrowth's mid-game power makes you incredibly scary to the enemy team when you've hit 2 items, able to chase down any target.
Death by Steel
Lane harassment and consistent damage output.
- Predator
Add an active effect to your boots that grants a large boost of
MS and causes your next attack or ability to deal bonusadaptive damage . 
Cheap ShotDeal bonus true damage to enemy champions with
impaired movement or actions .
Grisly MementosCollect 1 memento on champion
takedowns , up to 18 total.
Gain 6 Trinket Haste for each collected.- Ingenious Hunter
Unique
takedowns grant permanent ItemHaste (includes Trinkets).
Sorcery
Empowered abilities and resource manipulation
Nimbus CloakAfter casting a Summoner Spell, gain a short
Move Speed increase that allows you to pass through units.
WaterwalkingGain
MS and AP or AD,adaptive in the river.
Adaptive Force
+9
Adaptive Force Adaptive Force
+9
Adaptive Force Health Scaling
+10-180 Health (based on level)
Why Predator
Predator on Olaf allows you to hit the go button on ganks and not let up. With the CC immunity from [R] you'll be hunting down anyone who gets in your way.
Why Cheap Shot
Cheap Shot allows your to repeatedly deal True Damage to whatever target your attacking thanks to the **perma-slow from [Q] and Righteous Glory**.
Why Grisly Mementos
Grisly Mementos on jungler provides massive amount of vision thank to your natural deep warding to keep track of the enemy jungler, as well as clearing of enemy wards with Sweeper/Control Wards.
Why Ingenious Hunter
The item CDR from Ingenious Hunter allows you way more uses of Predator and Righteous Glory for those unstoppable ganks.
WhyNimbus Cloak
Nimbus Cloak's burst of Movement Speed synergizes well with Olaf's [R] playstyle when looking to chase down a target.
WhyWaterwalking
Waterwalking's jungle control power and mobility is huge for contesting crabs and dragons.