Semi-Analytical Solutions of Classical Free Boundary PDEs Using HAM with MAPLE and MATLAB presents a practical, reproducible framework for solving moving-boundary (Stefan-type) partial differential equations using the Homotopy Analysis Method (HAM). The book develops a step-by-step semi-analytical workflow that couples the temperature field with interface evolution, emphasizing timewise determination of the convergence-control parameter and accurate reconstruction of the free boundary. Implementations in MAPLE (symbolic construction) and MATLAB (numerical verification) are included to support full reproducibility of tables and plots. Designed for researchers, graduate students, and practitioners in applied mathematics and computational science, this monograph provides a clear pathway from model formulation to validated semi-analytical solutions for classical free boundary PDE problems.