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I can't add android support design library to my project because "This support library should not use different version (26) than the compileSdkVersion (25)". But my android SDK version is 26.0.2. and when i try to change sdk version to 26 in gradle it gives me error. So why Android Studio can't use the latest sdk version? Here is the
screenshot.

But my android SDK version is 26.0.2
There is nothing in that screenshot with a value of 26.0.2.
There is a 25.0.2, and that is your buildToolsVersion, which is not your problem.
So why Android Studio can't use the latest sdk version?
Android Studio can.
Your Gradle build file is attempting to use a preview edition of com.android.support:design. That specific version, 26.0.0-alpha1, begins with 26. The rule with the Support Library is that your compileSdkVersion needs to match that major version number of the library. In your case, your compileSdkVersion is 25.
The simplest solution for you is to change your compile statement to:
compile 'com.android.support:design:25.3.1'
This solves two problems:
It synchronizes the major version of the library with your compileSdkVersion
It gets you on a production-ready version of the library, rather than an alpha1 preview release, tied to the Android O developer preview