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 TypeScript, and analyze their complexities. Stacks are used in various real-world applications, such as undo operations in text editors. 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. In a LIFO stack, the last item added is the first removed. For example, adding numbers 1, 2, and 3 in sequence will yield removal in the order: 3, 2, 1. Let's see an implementation in TypeScript, where we'll push (add), pop (remove), and peek (view the top) elements.

We start by introducing the Stack class that stores an array of items that are of a specific type. Utilizing a generic type <T> makes the stack versatile, allowing it to handle any data type, such as numbers, strings, or custom objects.

In TypeScript, 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.

Let's look at how our operations look implemented in code: