multiproject gradle build error: package does not exist

Your app module's build.gradle should contain (among other things)

apply plugin: 'com.android.application'
dependencies {
    compile project(':my_library_module')
}

Your library module's build.gradle file should contain

apply plugin: 'com.android.library'

If you're using Core as library you should change apply plugin: 'android' to apply plugin: 'android-library' in App/libraries/Core/Core/build.gradle

To resolve the package not found errors, in the app module's build.gradle file I added

dependencies {
    // ...
    compile project(':library')
}

which adds the library module as a dependency to the app module