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What is the difference between an activity going in the background and an activity becoming invisible?

I am new to android.I have learned that the onPause() method is called when some other activity comes in the foreground and onStop() method is called when an activity is no longer visible.Can someone please explain what's the difference between going in background and becoming invisible giving some practical example.

Best example? A popup, your activity is still visible, so only onPause() is called. Becoming invisible is when another activity is launched, the app is sent to the background, the user switches to another app et.

Think about two cases
1. Calling Activity B as dialog
In this case, some part of Activty A will be visible. So only onPause() method will get called for Activity A. And when you will be back from Activity B to A, onResume() of Activity A will get called.
2.Calling Activity B as normal activity
In this case, Activity A will be completely invisible, So onPause() and onStop() both will be called. And when you will be back from Activity B to A, onRestart(), onStart() and onResume() methods of Activity A will be called.
Have a look
Case 1: If you call normal activity. (Which is going to hide caller activity)
onPause()
onStop()
<------- Back to caller
onRestart()
onStart()
onResume()
Case 2: If you call activity-as-dialog. (Which is going to partially hide caller activity)
onPause()
<------- Back to caller
onResume()

whenever a dialog box appears on any activity then activity's onPause() called and this activity holds the first position in stack(Top), on the other hand whenever we switches activity from one to another the previous activity's on Stop() method called and its automatically garbage collected in sometimes.

when onStop is actually called

In my simple android app I have 2 activities. In first activity(Main activity) I have override the ON STOP method. But when I go do the second activity on stop method of main_Activity is called. Why this happens? According to my understanding I should call on Pause rather then on Stop.

It calls both. onPause() will be called before onStop(), if onResume() was called. Rougly speaking, onPause() is called when activity is partially hidden, and onStop() when it is fully hidden.
Read up on http://developer.android.com/training/basics/activity-lifecycle/index.html to understand the Activity lifecycle.

onPause() - activity is paused.
onStop() - activity is stopped working but it is there in stack.
onDestroy() - activity is stopped and also has been removed from stack.
therefore When you go from one activity to another activity, it makes onPause() and onStop() but not onDestroy()

OnStop is called when FirstActivity calls SecondActivity and FirstActivity looses
visibility.
If Second Activity has a transparent background then the FirstActivity will be visible underneath, so not loosing visibility and onStop on FirstActivity will never be called.

Life cycle of Android Activity after pressing Back button

I am little confused between the life cycle of two activities.
Suppose I have Activity A and Activity B.
B is called From A i.e A ----> B.
Now currently B is on the screen and I pressed back button. Here I want know:- is there any memory still available for B(Active) or B's memory is flushed(Inactive).

The following activity call back methods are called, after pressing back button.
onPause()
onStop()
onDestroy()
The activity is destroyed.
And it recreates when launched again. These are the callback methods when it launches again.
onCreate()
onStart()
onResume()

I know the answer is been accepcted, still if this helps someone I am putting it.
When app is opening for the first time, by clicking the Icon
onCreate()
onStart()
onResume()
When home button is pressed
onPause()
onStop()
when app is again opened by clicking the app icon or launched from recent
onRestart()
onStart()
onResume()
when app is opened and then back button is pressed
onPause()
onStop()
onDestroy()

The onDestroy method is called after back press. Then activity will be popped from the Activity back stack.
From docs:
If an activity is paused or stopped, the system can drop the activity from memory by either asking it to finish, or simply killing its process. When it is displayed again to the user, it must be completely restarted and restored to its previous state.
onDestroy() from docs:
The final call you receive before your activity is destroyed. This can happen either because the activity is finishing (someone called finish() on it, or because the system is temporarily destroying this instance of the activity to save space. You can distinguish between these two scenarios with the isFinishing() method.

Activity B will be destroyed and will no longer remain in memory.
For more information please visit the official documentation for android and have a look at the activity life cycle figure.
Once you press the back key the activity's onDestroy() method will be called and the activity will be flushed out of the memory. You will then be required to restart the activity by calling the startActivity() method which will in turn call its onCreate() Method.

I would suggest to refer following link for activity lifecycle
http://stackoverflow.com/a/8516056/3110609
and following link for launch mode of activity.
www.intridea.com/blog/2011/6/16/android-understanding-activity-launchmode

After pressing the back button, Activity B will b destroyed. You see, Android Manages Activities like a Stack(an explanation of a stack). Everytime you start an activity, it pushes into the Activity Stack. So when Activity A calls Activity B, Activity B is now on top of Activity B, and when you press the back button, it also does a pop in the Activity Stack. So in concept, Activity B is gone. Pressing a Home Button is different from pressing back, it pauses the Activity, therefore it still eats a little of the phone's memory.
Here is a good explanation of how Android Manages Activities.

Android Activity-Lifecycle... how to avoid onDestroy()?

I have an App, which uses an ActicityGroup to have a stack of Activitys. If I start a new Activity, I do this as Child of my ActivityGroup. Lets assume I'm in my starting Activity (1), and I start a new one(2), so here is what's getting called:
(1): onPause()
(2): onCreate(), onStart(), onResume()
until here, everything as aspected. if I press my BackButton the stack is as following:
(2): onPause(), onStop(), onDestroy()
(1): onStop(), onDestroy() [sic]
(1): onCreate(), onStart(), onResume()
I see no reason,first why (1) should perform onStop, and onDestroy(), to reCreate again, and second why onRestart never gets called on (1).
Has anyone a Reason for this behavior? Can I 'cancel' calls to onStop() or onDestroy() somehow?
any idea apreciated

Try using FLAG_ACTIVITY_SINGLE_TOP when starting child activity, like:
Window window = getLocalActivityManager().startActivity(id,
intent.addFlags(Intent.FLAG_ACTIVITY_SINGLE_TOP));
More info here:
http://developer.android.com/reference/android/content/Intent.html#FLAG_ACTIVITY_SINGLE_TOP

You can avoid Activity onDestroy method when back button pressed in a very simple way,
Just mention
android:persistent="true"
for your activity, that should prevent your activity getting destroyed, To know more in detail you can visit the below SO post
Prevent activity from being destroyed as long as possible

when you press back button it's default behavior is stop or destroy the current activity you can override the back button. If you press home button then it will use the onPause() that means os will consider that you want to continue with current activity when you again launch same activity but if you press back button it means that you finish your current activity and back to the last activity

Onstop() and onDestroy() will not call untill you did not finish activity. Ondestory() called for releasing of resource that occupied by Activity. IF activity use has been over then it is better to destroy this activity.
Second it will be good for memory management scheme. and if you do not call destroy then it will automatically call when you exit from app
and finally
if you doesnot want to call destroy when you press back button then you can use override method onBackpressed()

Life cycle called when backpress is pressed to navigate back to the previous activity?

What activity state is called when another activity, in the same application, is launched, and then the backpress button is clicked to navigate back to it?
What lifecylce method is called during the proccess of going back to the previous activity?

onPause() is called in Activity A when it launches Activity B. After the back button is called in Activity B, onResume() is called in Activity A.

What lifecylce method is called during the proccess of going back to
the previous activity?
According to the docs: onPause(), onStop(), and possibly onDestroy(). In addition to the lifecycle documentation, you might want to read the docs on Tasks and Back Stack.