This collection consists of selected scientific results stemming from the conference "e;Methusalem Workshop on Classical Analysis and PDEs"e;, held at the Ghent University from 27th February 2023 to 1st March 2023. The workshop was organized by the "e;Ghent Analysis & PDE Center"e;. 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.