Gradle DSL method not found: ‘compile()’

As the note of your project’s build.gradle file suggests:

// NOTE: Do not place your application dependencies here; they belong
// in the individual module build.gradle files

Remove the 2 compile statements in that gradle file:

compile 'com.android.support:appcompat-v7:20.+'
compile 'com.google.android.gms:play-services:6.5.+'

And then make your other (module’s) build.gradle dependencies look like this:

dependencies {
    compile fileTree(dir: 'libs', include: ['*.jar'])
    compile 'com.android.support:appcompat-v7:21.0.3'
    compile 'com.google.android.gms:play-services:6.5.+'
}