This book displays the latest developments in the determinatioin of the electronic structure of solids and the physical properties which can be described from the electronic structure. Special emphasis is placed on the Linear Muffin Tin Orbital method for ground state and excited state calculation. The state-of-the-art of the formalisms is presented, from the venerable Atomic Sphere Approximation to the Full Potential schemes. The efficiency of this method is shown in various situations: magnetic properties, interlayer exchange coupling, metallic alloys, d- and f-electron systems. The latter part of the book is devoted to large-scale real-space calculations, including an introduction to sparse direct methods. With the aim of maximizing tutorial value, experts in each domain present over ten years of work, which has been published only in specialised papers before and now becomes available for researchers as well as students and teachers in solid state physics or materials science.