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You must own Chivalry to use the SDK. The SDK build is a branch of Chivalry that includes an editor; it's the full game and can be used for both creating a testing/playing custom content. Eventually, this branch will be merged with Chivalry-proper and moved out of the Beta. You can't join non-SDK-branch servers from the SDK branch, and vice-versa, so until that merge happens both custom content creators and testers/players need to be using this branch.
To download the SDK build, open up your Steam Library, right click on Chivalry: Medieval Warfare Beta and go to Betas. Choose the SDK beta. You'll then be subject to a ~3-5 GB download. If you ever want to switch back to the normal Chivalry Beta, you'll again be subjected to a large download. This will be true every time you try to switch between the two.
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