The release of the youtube video for the London Theory institute seminar series https://youtu.be/jTRQTwBX9ek. In this introductory lecture we describe the XXX Heisenberg spin chain, study its spectrum, wavefunctions and discuss integrability of the system. Some examples are given with simple Mathematica code. We also discuss applications to AdS/CFT correspondence. Some derivations are formulated in the form of step-by-step exercises. They can be solved either with Mathematica or by hand. A quick introduction to Mathematica is provided in a separate video.