I have a map between string and a class object. I populate this map in Activity1 and i would like to pass it to activity2.
public class NEW extends Activity
I am assuming you own both Activities (call them A and B). In which case just put the map in a public static variable and access it from B via A.data_map.
[update]
For all of the downvotes take a peek at the Android Application Framework FAQ section "How do I pass data between Activities/Services within a single application?". The solution I recommend is exactly the same as...
A public static field/method
An alternate way to make data accessible across Activities/Services is to use public static fields and/or methods. You can access these static fields from any other class in your application. To share an object, the activity which creates your object sets a static field to point to this object and any other activity that wants to use this object just accesses this static field.
Yes, there are caveats to this solution but with the limited info presented by the OP we can not assume this method will not work.