This is the live session included as part of the LonTI lecture on "From spin chain to AdS/CFT with Mathematica". Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. ​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.