Whether you are counting the number of apples you have in your basket or measuring the properties of subatomic particles at CERN, numbers pervade your life in some way or another. But what is a number anyway? What do we really refer to when we say “$$ 4 $$”? What about “$$ \frac{2}{3} $$”, “$$ \sqrt 2 $$”, and “$$ \pi $$”? In this course we rigorously construct the systems of numbers that we have come to take for granted. We begin from the most basic structures in mathematics, sets, and systematically construct the natural, rational, and real numbers, using techniques from different areas of mathematics. Along the way, we explore some of the fascinating properties of these number systems that have given rise to whole new fields in modern mathematics. Join us in building mathematics from the ground up!