Description and Basic Story here in the beginning. If only item-build is in your interest, feel free to bypass the wall of text and scroll right down.
Enjoy the guide, and thanks for reading.
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The almighty and mighty underestimated hard-carry, Medusa the Gorgon. Few fear her, many underestimate her, after her recent change or not. In this guide, I'm aiming to shed light on just exactly WHY Medusa has what it takes to role with the best of them.
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The Story of Medusa in DotA

Back in the days of DotA 1, Medusa was in her prime-time pickingwise. The powerful snake lady was feared by everyone, and when she wasn't picked, she was close-to-always picked, due to her immense tankability and power dishing damage as a carry hero. Because Medusa was such a problem back then, teams began speculating just how they should ever be able to counter such a strong hero.

People came up with the back then underrated ANTI-MAGE as the best possible counter to Medusa, and rightfully so, after people realised just how good of a counter Anti-Mage was, Medusa the Gorgon dispersed in his might. This also explains why exactly Anti-Mage got extremely popular, not just as a counter, but as a previously over-looked hero.
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Medusa - The Serpentine Carry

Medusa is an odd-case of a hero. Looking at Medusa's skill, it shouldn't take long for the average player to find out that she's definitely hardcore carry material, with the ability to both sustain tremendous amounts of punishment, as well as dishing out a fiery wrath of power back at her enemies.
If we look towards Medusa as a hero from the beginning, she's lackluster to say the least. Her damage is terrible, her animation isn't exactly the best, and her stat gain per level is definitely sub-par at best, so you might be asking yourself, why would you ever pick Medusa if she's such a weak hero from the get-go?

-POWER-

While it is certainly true that Medusa's early capabilities are rotten, she shines in the same way that other carries like Faceless Void does. Level's are not what make Medusa a fearful hero, but rather, it's the items. With herself stashed up to boot, Medusa will be able to crush almost any opposition in-front of her, making people regret they ever let her farm to begin with.

Thus, if you truly wish to pick up Medusa, you should be mindful about just HOW much you need to farm with this hero. Level's wont cut it, but gold will. You will be a sitting duck with the occasional harassment of your Mystic Snake, and your primary form of teamfight will come from your ultimate. However, given time, you will blossom into an unstoppable form of epic porportions that will lay waste to any and every enemy on the battlfield.

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WARNING:
The Reader should know before-hand that picking Medusa up in a public setting can be a hard thing to accomplish, considering the circumstances at which Medusa proves useful as a hero. Medusa needs time and farm beyond any other carry! Due to the low patience factor that is common in public games within DotA 2, you may have a hard time reaching Medusa's potential. It's safe to say that your allies will have to do decently without you for quite some time.