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This book consists of two parts. The first part aims to explore the application of the popular method of the finite element method (FEM) in the electronic structure theory. The finite element method is a very general numerical technique in mathematics for solving partial differential equations (PDEs) and it has been widely applied in computational mechanics and engineering in general, but it has not been extensively used in science for electronic structure calculations. In the second part of the book, special attention has been paid to carbon nanotubes (CNTs) and their thermo-electro-mechanical properties. Application of CNTs and other carbon-based materials such as graphene in science and technology has been constantly on the rise in the past two decades for example as wires, switches, transistors or other nano-electro-mechanical systems (NEMS) and nanostructures. Here, several of the more fundamental mechanical, chemical, heat transport and thermal properties of the CNTs for these applications and for microscopy purposes (in particular, atomic force microscopy or AFM) have been computationally as well as experimentally studied.