I am using a textbook which uses android V2.0. Can you tell me which version of android can run apps for version 2.0 without any problems ?
If you are going for just running the app, then any device with API level 5 (Android 2.0) and up (that includes Jelly Bean and any future versions) will be able to run your app without any problems. The developer docs have an API level guide here.
However, you should familiarize yourself with subsequent versions of Android so that you can make an informed decision on what version you should use, and what features you will be unable to use.
For example, you can see on the Supporting Multiple Screen Sizes page that Android 3.2 (API level 13) introduced new features for supporting multiple screen sizes. If you use API level 5, your application may not scale correctly on some devices (namely tablets).
Though it is tempting to try to support as many devices as possible, there is a definite trade off involved with using a lower API level. For some apps, it doesn't really matter if it scales correctly, but it is something that you need to take into consideration when choosing a target or minimum API level.