Hash Maps, or Hash Tables, are associated containers that are formed with a key value and a mapped value, allowing for fast retrieval of elements based on their key. A hash function computes the index in the array to store the values. Chaining and Quadratic probing are collision resolution techniques. Chaining appends colliding keys to one another. Quadratic probing finds the next open bucket by computing the hash and adding i^2 until an open bucket is found. The success of a Hash Table depends on how well the hash function assigns unique keys to unique buckets.