Q:

Why does arraylist class implement List as well as extend AbstractList?

The implementation of java.util.ArrayList implements List as well as extends AbstractList. But in java docs you can see that AbstractList already implements List. Then wouldn't it be redundant to implement List as well as extend AbstractList?

My second question 

Please have a look at the following code : 
String str = "1,2,3,4,5,6,7,8,9,10";
String[] stra = str.split(",");
List<String> a = Arrays.asList(stra);

The Arrays.asList() method of the Arrays class contains its own implementation of ArrayList. But this one only extends AbstractList but does not implement List. But the above code compiles.
BUT when the code is modified to the following 
String str = "1,2,3,4,5,6,7,8,9,10";
String[] stra = str.split(",");
java.util.ArrayList<String> a = Arrays.asList(stra);

I get an error : cannot convert form List<String> to ArrayList<String>

What is the reason behind this?

EDIT
Arrays.asList() does return its own implementation of ArrayList. Check this out.

A:

Then wouldn't it be redundant to implement List as well as extend AbstractList?

Yes, it is 100% redundant. However, Java implementors added interfaces very consistently in all public implementation of the collections library:

LinkedList<E> and ArrayList<E> extend AbstractList<E> which implements List<E>, and then implement List<E> themselves.
HashSet<E> and TreeSet<E> extend AbstractSet<E> which implements Set<E>, and then implement Set<E> themselves.
HashMap<K,V> and TreeMap<E> extend AbstractMap<K,V> which implements Map<K,V>, and then implement Map<K,V> themselves.

My understanding is that they did so for documentation purposes:  the authors wanted to show that ArrayList<E> is primarily a List<E>; the fact that ArrayList<E> extends AbstractList<E> is a less significant detail of its implementation. Same goes for the other public collection types.
Note that Arrays.ArrayList<E> class is not publicly visible, so its authors did not care to include List<T> explicitly.
As far as the failed conversion goes, this should come as no surprise, because the inner class Arrays.ArrayList<E> and the public class ArrayList<E> are unrelated to each other.

A:

For your first question take a look at Why does ArrayList have "implements List"?

To answer your second question 
java.util.ArrayList<String> a = Arrays.asList(stra);

as you mentioned Arrays.asList returns its own implementation of AbstractList and unfortunately creators of this code also named this class ArrayList. Now because we cant cast horizontally but only vertically returned array list can't be cast to java.utli.ArrayList but only to java.util.AbstractList or its super types like java.util.List that is why your first code example works.

A:

Arrays.asList returns a List. So casting it to ArrayList is not safe as you do not  know what type of List is being returned (depends on the array type it's creating the list from). Your second snippet wants an ArrayList implicitly. Hence it fails while your first snippet compiles fine because it expects a List. You can do-
ArrayList<String> a = new ArrayList<String>(Arrays.asList(stra));

