Topological Insulators -- A review

These lecture notes were prepared for a mixed audience of students, postdocs and faculty from the Indian Institute of Technology Madras, India and neighboring institutions, particularly the Institute of Mathematical Sciences. I am not an expert on the subject and during the few years I spent working on the Quantum Hall effect, I had not fully appreciated that it was part of a family of topological insulators. It was a pleasure to dig a little deeper into this subject and to share its wonders with others. In preparing these lectures I relied heavily on the help of Ganpathy Murthy (UKy) and a very helpful conversation with Steve Kivelson (Stanford.) I am of course responsible any errors despite their efforts. I also relied on some excellent Powerpoint slides of various talks. I have furnished a few choice references at the end and very few references to original papers. I cover only $d=1$ and $d=2$.