This collection consists of selected scientific results stemming from the conference "Methusalem Workshop on Classical Analysis and PDEs", held at the Ghent University from 27th February 2023 to 1st March 2023. The workshop was organized by the "Ghent Analysis & PDE Center". The presented materials mainly consist of scientific results on classical analysis and problems of PDEs. In particular, results on harmonic analysis, functional spaces, functional inequalities, inverse problems, non-local PDEs, non-classical problems of PDEs, integro-differential equations, hypoelliptic operators, pseudo-differential calculus, and others are given.