This one is a simple Olaf build with offensive abilities. It focuses on having a high physical damage output and some critical strike chances, while maintaining high hp. Olaf's innate ability is Berserker Rage, so it gives an %40 - 50% attack speed bonus at %60 - %50 health, which is actually around 1500-1600 hp (quite enough to survive), since we are using Warmog's armor as a good health source, around levels 12-13.

In this build, the skill progression is focused on maxing Reckless Swing as soon as possible, because this skill is especially useful on early levels, while the opponents don't have that much health, so the true damage dealt using this skill, without mana cost and low cooldown can increase your kill/assist score granting you additional gold. In end game this skill is not much effective, because it doesn't have any bonus damage scaling with AP, bonus physical damage etc, it is not much more than your standard attack (even lower than your critical attack).

Secondly I have concentrated on Tough It Out because in mid-late game, survival in a 5v5 fight is more important and this skill ensures that you have a decent amount of life steal (combined with your Emblem of Valour ) also converting %1 of your hp to attack damage, so it feels like you have another Atma's Impaler in inventory for 6 seconds.

Undertow is a nice skill, with slow and very good range, but I don't find it usefull for upgrading more than 2 (maybe 3) since the other abilities seem to be far more useful.

Ragnarok is Olaf's ulti, it gives a quite usefull passive armor penetration, so it is to be upgraded when possible (at lvl 6, 11 and 16).

For the runes I prefer Greater Mark of Desolation and Greater Quintessence of Desolation, but of course one of these sets can be switched to Greater Mark of Attack Speed, or Greater Quintessence of Attack Speed. Since survival in this game is quite important, I preferred Greater Seal of Armor and Greater Glyph of Magic Resist, but in case you require more health at start-up you can easily switch to Greater Seal of Vitality(or Greater Quintessence of Health), or Greater Glyph of Cooldown Reduction if you want to spam skills a little more frequently.

The item build is based on concentrating on health firstly (using Warmog's Armor), mainly because of spammable [Reckless Swing] easily on early levels, and to increase damage and life steal for survival in later levels. Of course depending on your opponents, you can easily switch Mercury's Treads to Ninja Tabi to provide dodge and armor, also if you prefer more attack speed and armor reduction you can switch Bloodthirster to Black Cleaver or if you want additional survival ability you can switch it to Banshee's Veil.

Most of the builds recommend Frozen Mallet, it is a good item, since it's passive slows opponents and makes it easier for Olaf to catch them, but compared to the damage and life steal of Bloodthirster, I found it less preferable. It would make a great source of additional health, though.

Since this is supposed to be an offensive build, I tried to max the offensive tree, leaving only Brute Force at 2 (I don't think 1 additional damage is so important).

The rest goes to the utility tree, using Perseverence only for reaching the next tier of masteries. Also I gave 1 point to Utility Mastery because as a physical damage champion you should use the red buff frequently throughout the game.

For people who would prefer Ghost as a summoner spell can skip Perseverence totally, to get Haste .

This build is generally a tanky physical dps Olaf build, with some survival abilities. Olaf is a hard champion to play, especially it can very challenging to keep the hp ratio constant while maintaining a decent attack speed, to push towers, to get minion kills (earn money) and of course get opponent kills/assists.

I am quite new to Olaf, (around 30-40 matches roughly), so this build may have flaws or may lack useful information, any positive criticism is appreciated.

Thanks for reading and commenting.