This book is the second edition of <i>Numerical methods for diffusion phenomena in building physics: a practical introduction</i>&nbsp;originally published by PUCPRESS (2016). It&nbsp;intends to stimulate research in simulation of diffusion problems in building physics, by providing an overview of mathematical models and numerical techniques such as the finite difference and finite-element methods traditionally used in building simulation tools.&nbsp;Nonconventional methods such as reduced order models, boundary integral approaches and spectral methods are presented, which might be considered in the next generation of building-energy-simulation tools.&nbsp;In this reviewed edition, an innovative way to simulate energy and hydrothermal performance are presented, bringing some light on innovative approaches in the field.