Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin

These lectures give a basic introduction to $\mathcal{N}=4$ SYM theory and the integrability of its planar spectral problem as seen from the perspective of a recent development, namely the application of integrability techniques in the study of one-point functions in a defect version of the theory.