Hello, eager learners! In today's lesson, we're exploring Stacks, a crucial data structure in programming. We aim to understand Stacks, implement and manipulate Stacks in JavaScript, and analyze their complexities. Let's dive right in!

First and foremost, let's understand what a Stack is. Imagine a stack of plates that you can only remove from the top. This concept exemplifies Stacks, which follow a Last-In, First-Out (LIFO) structure. Let's see an implementation in JavaScript, where we'll Push (add), Pop (remove), and Peek (view the top) elements.

We start with introducing the stack class that stores an array of items.

In JavaScript, arrays can work as Stacks. They have the necessary built-in methods. However, let's implement each operation ourselves to understand this data structure better.

The Push operation adds a new element to the top of the Stack. It is simply written as:

The Pop operation removes the topmost element from the Stack. It first checks if the Stack is empty, then returns "Underflow". Otherwise, it removes and returns the top element of the Stack.

The Peek operation lets us view the topmost element without removing it.

The Push, Pop, and Peek operations take constant time — O(1). This is because these operations are performed at the end of the array. The space complexity is proportional to the number of elements — O(n), where n is the quantity of Stack elements.

Here is a complete stack implementation with usage example:

However, in JavaScript we usually don't implement stacks ourselves or use any special object for it. Instead, we simply use arrays as stacks:

Well done! You've completed your journey through Stacks in JavaScript, mastering their concept, implementation, operations, and complexity analysis. Exercise sessions await you to strengthen your skills further. So, let's set sail for some exciting hands-on practice!