How does one numerically analyse different phases of liquid crystals? With the help of some open-source libraries, what can we do in exploiting the mathematical models of liquid crystals and numerical aspects of their typical defects? There are many excellent books on liquid crystals, but none on their numerics to the knowledge of the author. This book presents some of the latest work on numerical investigations of liquid crystals, addressing some mathematical modelling and numerical problems. This book consists of three major parts, each of which focuses on different problems for different phases of liquid crystals: nematics and cholesterics, ferronematics and smectics. The associated topics include robust solvers for cholesterics, multiple solutions for ferronematics, and mathematical modelling theory for smectics, etc. This interdisciplinary book can be helpful in utilising the open-source libraries Firedrake (for solving problems using finite element methods) and Defcon (for computing multiple solutions) to solve general energy minimisation problems. Sample Chapter(s) Preface Chapter 1: Introduction Chapter 2: A Mathematical Model of Nematics and Cholesterics Contents: Introduction Nematic and Cholesteric Liquid Crystals: A Mathematical Model of Nematics and Cholesterics A Robust Multigrid Algorithm for the Augmented Director Block Numerical Experiments for Nematics and Cholesterics Ferronematic Liquid Crystals: A Mathematical Model of Ferronematics Computing Multiple Solutions Using Deflation Numerical Verifications for Ferronematics Smectic Liquid Crystals: A Mathematical Model of Smectics Finite Element Discretisation Numerical Experiments for Smectics Conclusions and Perspectives: Summary and Conclusions Appendices: Stability of the Newton System Equilibrium Equations in Two Dimensions Readership: Advanced undergraduate and graduate students interested in numerical modelling of liquid crystals; researchers in the fields of mathematical theories and numerical aspects in liquid crystals.