This is an introductory course on an exciting field of modern mathematics which has many applications. Topics will include: What is a chaotic system? What makes a system chaotic? Fractals; drawing fractals, fractals in nature. Strange attractors. Julia sets. The Mandelbrot set - and more. Along the way we will look at the historical development of these ideas and how they are used today in areas such as physics, biology, medicine, and economics.