what are Absract Data Types ?

An abstract data type (ADT) is a mathematical model for data types, where a data type is defined by its behavior (semantics) from the point of view of a user of the data, specifically in terms of possible values, possible operations on data of this type, and the behavior of these operations. This contrasts with data structures, which are concrete representations of data, and are the point of view of an implementer, not a user.
In simple words ADT can be defined as a user defined data type whose operations for read / write are defined by the programmer in the form of functions.

Types of Abstract Data Types :
1) Associative array, map, symbol table, or dictionary is an abstract data type composed of a collection of (key, value) pairs, such that each possible key appears at most once in the collection.

Operations associated with this data type allow:

• the addition of a pair to the collection
• the removal of a pair from the collection
• the modification of an existing pair
• the lookup of a value associated with a particular key

2) Set : In computer science, a set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set.

Operations : basic add / remove operations:

• create(): creates a new, initially empty set structure.
• create_with_capacity(n): creates a new set structure, initially empty but capable of holding up       to n elements.
• add(S,x): adds the element x to S, if it is not present already.
• remove(S, x): removes the element x from S, if it is present.
• capacity(S): returns the maximum number of values that S can hold.

Core set-theoretical operations:

• union(S,T): returns the union of sets S and T.
• intersection(S,T): returns the intersection of sets S and T.
• difference(S,T): returns the difference of sets S and T.
• subset(S,T): a predicate that tests whether the set S is a subset of set T.

3) Linked List ,Stacks and Queue's : Stack is basically a data structure that follows LIFO (LAST IN FIRST OUT). Queue is one which follows FIFO (FIRST IN FIRST OUT). In general, Stacks and Queues can be implemented using Arrays and Linked Lists.

Operations on stack and queues implemented using linked list : 

• push and pop elements in case of stack
• enqueue and dequeue in case of queue

4) Tree Data Structure : In computer science, a tree is a widely used abstract data type (ADT)—or data structure implementing this ADT—that simulates a hierarchical tree structure, with a root value and sub tree's of children with a parent node, represented as a set of linked nodes.

Operations on Binary Tree : 

• Searching: For searching an element , we have to traverse all elements (assuming we do breadth first traversal). Therefore, searching in binary tree has worst case complexity of O(n).
• Insertion: For inserting an element as left / right child , we have to traverse all elements. Therefore, insertion in binary tree has worst case complexity of O(n).
• Deletion: For deletion of  an element , we have to traverse all elements to find it (assuming we do breadth first traversal). Therefore, deletion in binary tree has worst case complexity of O(n).

if any doubts or queries please comment