This book amalgamates geometric modelling, analysis and optimization, the three important aspects in Computer Aided Engineering Design. While the three subjects are well developed by themselves, a detailed discussion on engineering visualization (transformations and projections) and mathematical background of free form, parametric and piecewise design of curves and surfaces is provided. A topological basis is given when discussing wireframe, boundary representation and constructive solid geometry as solid modelling techniques. Computational geometry, point membership classification and recent trends on modelling using point cloud data in reverse engineering are also covered in brief. The book provides an introductory treatment on linear elastic finite element analysis using some basic elements and optimization methods ranging from root finding single variable to constrained multi-variable approaches. The book is conceived with an intent to be a text for a semester course.