Here's an explanation of List in Java, its methods, and its implementation classes.

A List is an ordered collection of elements that allows duplicates. In Java, the List interface extends the Collection interface, and provides additional methods for working with lists.

In addition to the List interface, Java provides several implementation classes for working with lists. Here are some of the most commonly used implementation classes:

1. ArrayList (c):

This is a resizable array implementation of the List interface. It is a good choice when you need to perform random access to the elements in the list. These are the advantages of Using arraylist as compare to other collection implementation classes.

a. Fast random access: Since ArrayList is based on an array, accessing an element at a specific index is faster than some other List implementations, such as LinkedList.

b. Efficient memory usage: ArrayList only requires enough memory to hold the number of elements it currently contains, making it efficient for large lists with many insertions or deletions.

c. Support for dynamic resizing: ArrayList can dynamically resize its underlying array, so it can grow or shrink as elements are added or removed.

2. LinkedList (C):

If our frequent operation is insertion or deletion then LinkedList is the best choice to use. Underlying data structure of LinkedList is Double LinkedList. It has own their advantages. let's see:

a. Efficient insertion and deletion: LinkedList can add or remove elements from the beginning, end, or middle of the list in constant time, which makes it useful for applications that frequently modify lists.

b. Low memory overhead: LinkedList requires less memory than ArrayList because it doesn't store all elements in contiguous memory.

c. Easy to iterate: LinkedList's iterator can be used to iterate forward or backward through the list, which can be useful in some scenarios.

3. Vector (C):

This is a synchronized implementation of the List interface that is similar to ArrayList, but with synchronized methods. It is a legacy class that has been mostly replaced by ArrayList. Let's discuss the advantage of Vector:

a. Thread-safe: Vector is synchronized, which makes it safe to use in multi-threaded environments where multiple threads may access the same list.

b. Support for legacy code: Vector has been around since Java 1.0 and is still used in some legacy code.

c. Dynamic resizing: Similar to ArrayList, Vector can dynamically resize its underlying array as elements are added or removed.

4. Stack (C):

This is a subclass of Vector that implements a last-in, first-out (LIFO) stack of objects. It provides additional methods for pushing and popping elements from the stack.

a. Last-in, first-out (LIFO) data structure: Stack is useful for scenarios where the most recently added element should be the first one removed.

b. Easy to use: Stack provides simple methods for adding and removing elements, such as push() and pop().

c. Can be used for recursion: Because of its LIFO nature, Stack can be used to implement recursive algorithms, such as depth-first search.

When choosing an implementation class for a List, you should consider factors such as the expected size of the list, the frequency and type of operations that will be performed on the list, and whether thread safety is a concern.

Here are some of the methods provided by the List interface:

1. add(int index, E element): Inserts the specified element at the specified position in the list.

2. remove(int index): Removes the element at the specified position in the list.

3. get(int index): Returns the element at the specified position in the list.

4. set(int index, E element): Replaces the element at the specified position in the list with the specified element.

5. indexOf(Object o): Returns the index of the first occurrence of the specified element in the list, or -1 if the element is not found.

6. lastIndexOf(Object o): Returns the index of the last occurrence of the specified element in the list, or -1 if the element is not found.

7. subList(int fromIndex, int toIndex): Returns a view of the portion of the list between the specified fromIndex, inclusive, and toIndex, exclusive.

Overall, the choice of implementation class for a List depends on the specific requirements of your application. If you need fast random access and efficient memory usage, ArrayList is a good choice. If you frequently add or remove elements from the list, LinkedList might be a better option. If you need thread safety, Vector is a good choice, and if you need a LIFO data structure, Stack is a good option.