The purpose of this chapter is to understand how quantum particles react to magnetic fields. There are a number of reasons to do be interested in this. First, quantum particles do extraordinary things when subjected to magnetic fields, including forming exotic states of matter known as quantum Hall fluids. But, in addition, magnetic fields bring a number of new conceptual ideas to the table. Among other things, this is where we first start to see the richness that comes from combining quantum mechanics with the gauge fields of electromagnetism.

We sketch the highlights of Part I, which introduces the concepts of quantum field theory.

We discuss the physics of pseudomagnetic field,s which can be induced in graphene by applying strains, and show how they can be used to manipulate electronic transport through graphene heterostructures (strain engineering). We consider strain-induced pseudo-Landau levels, which were observed in graphene, and discuss the related valley quantum Hall effect. At the end of this chapter we demonstrate that a combination of strain and electric gating can open energy gap in electron spectrum of graphene which can be potentially interesting for applications.