Typesetting mathematical equations on the web has always been a challenge. HTML and CSS have limited capabilities when it comes to rendering mathematical symbols, functions, and notations. This is where KaTeX comes in - a fast and lightweight JavaScript library that enables you to typeset mathematical equations in web applications.

KaTeX is an open-source library that was created by Khan Academy, an online education platform that offers free courses in various subjects, including mathematics. The library was designed to make it easy for developers to include mathematical expressions in web pages without sacrificing performance.

KaTeX supports a wide range of mathematical symbols and functions, and it uses TeX as its markup language. TeX is a popular typesetting language that has been used in academia for decades to produce high-quality scientific documents. With KaTeX, you can create complex mathematical expressions with ease, and the library will render them beautifully on your web page.

To get started with KaTeX, you need to include the library in your web page. You can download it from the KaTeX website, or you can use a CDN. Once you have included the library, you can start creating mathematical expressions in your web page.

Here are some examples of how to use KaTeX:

```
<p>The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $c$ are constants.</p>
```

In this example, we're using KaTeX to typeset an inline equation. The equation is enclosed in single dollar signs, which tells KaTeX to render it as an inline element.

```
<p>The area of a circle with radius $r$ is given by: </p>
<p>$$A = \pi r^2$$</p>
```

In this example, we're using KaTeX to typeset a block equation. The equation is enclosed in double dollar signs, which tells KaTeX to render it as a block element.

```
<p>The derivative of $f(x) = \frac{1}{x^2}$ is given by:</p>
<p>$$f'(x) = -\frac{2}{x^3}$$</p>
```

In this example, we're using KaTeX to typeset a derivative equation with fractions and exponents.

```
<p>The sum of the first $n$ positive integers is given by:</p>
<p>$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$</p>
```

In this example, we're using KaTeX to typeset a summation equation with a limit and a fraction.

These are just a few examples of what you can do with KaTeX. The library supports a wide range of mathematical symbols and functions, including integrals, matrices, limits, and more. You can find a full list of supported symbols and functions in the KaTeX documentation.

In conclusion, KaTeX is a powerful tool for typesetting mathematical expressions in web applications. With its fast and lightweight design, it's a great choice for anyone looking to include math in their website or application. So why not give it a try and take your math to the next level?