It is somewhat implicit that the readers are familiar with the first course on solid state physics, which mainly deals with electronic systems and teaches us how to distinguish between different forms of matter, such as metals, semiconductors and insulators. An elementary treatise on band structure is introduced in this regard, and in most cases, interacting phenomena, such as magnetism and superconductivity, are taught. The readers are encouraged to look at the classic texts on solid state physics, such as the ones by Kittel, Ashcroft and Mermin.

As a second course, or an advanced course on the subject, more in-depth study of condensed matter physics and its applications to the physical properties of various materials have found a place in the undergraduate curricula for a century or even more. The perspective on teaching the subject has remained unchanged during this period of time. However, the recent developments over the last few decades require a new perspective on teaching and learning about the subject. Quantum Hall effect is one such discovery that has influenced the way condensed matter physics is taught to undergraduate students. The role of topology in condensed matter systems and the fashion in which it is interwoven with the physical observables need to be understood for deeper appreciation of the subject. Thus, to have a quintessential presentation for the undergraduate students, in this book, we have addressed selected topics on the quantum Hall effect, and its close cousin, namely topology, that should comprehensively contribute to the learning of the topics and concepts that have emerged in the not-so-distant past. In this book, we focus on the transport properties of two-dimensional (2D) electronic systems and solely on the role of a constant magnetic field perpendicular to the plane of a electron gas. This brings us to the topic of quantum Hall effect, which is one of the main verticals of the book. The origin of the Landau levels and the passage of the Hall current through edge modes are also discussed. The latter establishes a quantum Hall sample to be the first example of a topological insulator. Hence, our subsequent focus is on the subject topology and its application to quantum Hall systems and in general to condensed matter physics. Introducing the subject from a formal standpoint, we discuss the band structure and topological invariants in 1D.