Welcome to our insightful session, where we will delve into the inner workings of Java's HashSet structure. Our goal for today is to comprehensively understand how a HashSet operates under the hood, how to leverage these structures in practice, and to learn detailed information about its time and space complexities.

In the programming world, we often use a Set when dealing with a collection of unique items. HashSet in Java is a specific set type offering advantages, such as efficient membership checks and duplicate removal. Today, we will focus on this unique structure and its practical applications. Ready? Let's embark on this learning journey!

A HashSet is an intrinsic part of Java's collections framework. It is designed to store unique elements in an unordered manner. As a class derived from the AbstractSet class and implementing the Set interface, a HashSet doesn't conform to the order in which elements are added. This gives its users the freedom not to maintain any sequencing while ensuring every stored element is distinct.

A HashSet stands out among Set implementations due to its ability to eliminate duplicate data. This makes it highly efficient when we need to swiftly check if an item exists in a collection or when we want to store only the unique data. Let's consider this using a simple Java code snippet:

import java.util.HashSet;  

class Solution {
    public static void main(String args[]) {  
        // Instantiate a HashSet
        HashSet<String> set=new HashSet<String>();
        
        // Add elements to HashSet
        set.add("David");
        set.add("Alice");
        set.add("Bob");
        set.add("Alice");

        System.out.println(set);  // prints [Bob, Alice, David]
        System.out.println(set.size());  // prints 3
    }  
} 

In this example, despite adding "Alice" twice to our HashSet, we observe that "Alice" is included only once when we display our set to the console. Note that "Bob" is shown before "David" or "Alice", though it has been added the last. This happens because sets do not preserve the order of the elements.

Under its hood, a HashSet uses a hash table to manage all its elements. A hash table revolves around an array of buckets that store all items. A hash function is integrated to generate a hash code; the hashed key indicates the memory location where each element gets stored, accelerating the element storage and retrieval process.

In Java, the add(), remove(), and contains() operations in the HashSet class rely on the hash code of the object you're dealing with. When adding or fetching an object, the hashCode method computes a hash that points to a particular bucket where the object will be stored or found.

The ability of a HashSet to mitigate collisions can be demonstrated with the following example:

import java.util.HashSet;

class Solution {
    public static void main(String[] args) {
        HashSet<Integer> set = new HashSet<Integer>();
        
        // Add elements to HashSet
        for(int i = 0; i < 100; i++){
            set.add(i); 
        }
        
        // Access all elements
        for(int i = 0; i < 100; i++){
            if(set.contains(i)) {
                System.out.println(i + " found");
            }
        }
    }
}

In this example, we add numbers from 0 to 99 to the HashSet and then check whether each of these numbers is present in the HashSet. Thanks to the hashCode method, the lookup for all these operations is highly efficient, keeping our code execution fast.