Hello

So, this is my build for Riven solo top, I use it even in Ranked games, and I must say, I usually rule. I don't think there is a similar build, if there is, I didn't see it, since I started using this build through my own testings with Riven.

Here is a little image to prove that i'm not lying about using it in ranked and obtaining good scores

So, hope you like it.

In Noxus, any citizen may rise to power regardless of race, gender, or social standing - strength is all that matters. It was with committed faith in this ideal that Riven strove to greatness. She showed early potential as a soldier, forcing herself to master the weight of a long sword when she was barely its height. She was ruthless and efficient as a warrior, but her true strength lay in her conviction. She entered battles without any trace of doubt in her mind: no ethical pause, no fear of death. Riven became a leader amongst her peers, poster child of the Noxian spirit. So exceptional was her passion that the High Command recognized her with a black stone rune sword forged and enchanted with Noxian sorcery. The weapon was heavier than a kite shield and nearly as broad - perfectly suited to her tastes. Soon after, she was deployed to Ionia as part of the Noxian invasion.

What began as war quickly became extermination. Noxian soldiers followed the terrifying Zaunite war machines across fields of death. It wasn't the glorious combat for which Riven trained. She carried out the orders of her superiors, terminating the remnants of a beaten and fractured enemy with extreme prejudice. As the invasion continued, it became clear that the Ionian society would not be reformed, merely eliminated. During one bitter engagement, Riven's unit became surrounded by Ionian forces. They called for support as the enemy closed in around them. What they received instead was a barrage of biochemical terror launched by Singed. Riven watched as around her Ionian and Noxian alike fell victim to an unspeakably gruesome fate. She managed to escape the bombardment, though she could not erase the memory. Counted dead by Noxus, she saw an opportunity to start anew. She shattered her sword, severing ties with the past, and wandered in self-imposed exile - on a quest to seek atonement and a way to save the pure Noxian vision in which she believed.

''There is a place between war and murder / in which our demons lurk.''

Well, to be honest, the runes I put here, are the ones that I am currently using, but I know they aren't the most adequate for a top solo champ but... I started playing riven with these runes, that I had for AD champions, and it turned out SO WELL, that I never really felt the need to change. But I leave it to you here. If you want to try these runes, i can guarantee you, they work well, but if you want to change it to something more adequate for solo top, go ahead.

So, the first item I take is immediately Vampiric Scepter. I know, I know, your reaction right now is probably something like "WHAAAAAAT??? this guy is nuts!"

However, after many games played with riven, i find this to be very good. It gives you nice lane consistency, since you get your health back pretty fast from minions, and it also helps if you rush Wriggle's Lantern faster, which is the vital item for being a good solo top with riven. Once you have your lantern thingy, things get much easier, trust me.

Then, after wriggle's, you get Mercury's Treads ( Ninja Tabi if their team is massive AD, which probably will NOT happen if ur playing ranked games), and Giant's Belt, to be more tanky obivously. Immediately after that, you start builing for Bloodthirster, and, no, you DON'T SELL YOUR WRIGGLE'S LANTER! By now, you are probably asking "WHY??". And i clarify: from all the games i have played with Riven in solo top, i find myself carrying my team. Not because our AD carry is bad, or he is underfed. Nah, just because, if you do everything well, by the time you get this, Riven will be the most helpful champion on your team. You engage the fights, you stun,shield, ult, (you probably will have killed 1 champion before even activating your ult), save one of your team-mates with stun, and kill the rest of the bastards with your Wind Slash. You see, with something like 2200hp, 33% lifesteal, 100+ AD, stun(W) and shield(E), you can do whatever the hell you want with your enemies, and will still get out of it ALIVE!
The rest of the build is pretty much the usual for most Solo-top champions, so im not going to talk about it...

So, here I will explain why I do not have Atma's Impaler on my build.

Atma's Impaler

So, first off, to buy Atma's you would have to sell one of the previous items on the build. let's start by saying we sell Wriggle's Lantern.
By doing so, you will get:
+15 armor (Wriggle's already gave you 30, so the difference between Atmas and Wriggle's is 15)
+56 attack damage (With full build, you will have 3957 Health, so, from the passive of Atma's Impaler you get +79AD, and since Wriggle's gave you 23AD, the difference is 56)
+18% critical strike chance
On the other side, you will lose:
- 15% lifesteal
- That free ward you get from wriggle's, which is important, believe me, but nothing extraordinary I'll give you that.

So, selling Wriggle's Lantern to get Atma's Impaler is not such a bad idea, and will give you many bonuses, tough losing those 15% lifesteal will be hard. However, the thing is, you will almost never get so late in the game to reach the point completing the build, and being able to sell wriggle's and buy Atma's. If you do, It's your choice, buy it or not, depends on the type of game you are facing.

Another thing is, selling Bloodthirster to buy Atma's...
well, I think this is pretty much a dumb idea.
You see, the AD difference between both items, will be very low, since Atma's will be giving you 79, like mentioned before, and Bloodthirster will give you 60+1AD and 0.25% lifesteal for each kill you get, without dying. Well, my average scores with Riven are 8/1, 7/0, and stuff like that, Riven dies very few times, so she will get AT least 68AD from Bloodthirster without any problem, and 17% lifesteal
Now, as I see it, the only reason to sell Bloodthirster and buy Atma's, is if you want to get more tanky, since you will get +45armor, which will make you get a total of 152 armor. Pretty good.

So, everything is said, and frankly, it's up to you to decide wether to buy Atma's or not. I still think that the build works really well without it, but will undoubtedly work well with it too.

Ok, seriously, it's not hard to do solo top with riven. BUT, you WILL have to play carefully.

Go to your turret, just start by last hitting minions dont push, AND , this is IMPORTANT, know when to use your Ki Burst!!
In the early game, you can use this to completely destroy you opponent development. When you see he is about to last-hit the minion, Approach, and Ki Burst the **** out of him! If you're about the same HP as him, you can also use the opportunity that he is stunned to spamm Broken Wings on the guy (REMEMBER TO USE THE BOOST FROM Runic Blade TO YOUR BASIC ATTACKS!! seriously, it's a HUGEEE help!!).

Or, if you are low on hp, just use Broken Wings/ Valor to get away from him after you stunned.
Farm carefully until you hit lvl 6 and get your ulti Blade of the Exile, remember to ward importante zones, so you don't get surprised by their jungler.
When you get your ulti...Well, you will probably own, IF you know how to use it.
Let your opponent push the lane, then, when you see an opening, Stun him with your W, land 2-3 basic attacks, Use Valor, spamm Broken Wings, activate ulti, hit him more with your boosted attacks from your passive, and finish him off with your Wind Slash(R).

Well done, you have now taken the advantage and will own the game ;)

Ok, so, from what i have seen, i can tell you that Riven can be effective against ANY champion that she can face, but there are some who will give her a hard time:

• Malphite ok this guy will be quite troublesome, for two reasons, and those are: First one - Malphite has that ****ing shield popping up all the times, what makes him pretty hard.
  Second one - Malphite usually builds with ARMOR, and his damage goes up as he stacks it. So, much probably, malphite will have Thornmail as soon as he can, which will be tough for you.
  
• Nasus Not as tough as Malphite, but that life-steal from his passive will be pretty annoying and make it hard to bring him down. That, and his ultimate ofcourse, will be a nightmare for you. But if you don't let him farm as I told you before, you will be alright.
  
• Garen Okay, garen actually only is on this list because of the players who DON'T know how to play riven... You see, Garen is usually a very tough solo laner, but mostly because of his Judgment. So, if you just use your Ki Burst to stop it,and get away from it, you will be alright

1 warning: Olaf isn't on the list because... I never really had trouble with him. His Undertow is pretty easy to dodge with Valor and the rest, well, Riven can handle Olaf in one-on-one fights.