How to view the contents of an Android APK file?

Actually the apk file is just a zip archive, so you can try to rename the file to theappname.apk.zip and extract it with any zip utility (e.g. 7zip).

The androidmanifest.xml file and the resources will be extracted and can be viewed whereas the source code is not in the package - just the compiled .dex file ("Dalvik Executable")

It's shipped with Android Studio now. Just go to Build/Analyze APK... then select your APK :)

While unzipping will reveal the resources, the AndroidManifest.xml will be encoded. apktool can – among lots of other things – also decode this file.

To decode the application App.apk into the folder App, run

apktool decode App.apk App

apktool is not included in the official Android SDK, but available using most packet repositories.