This book provides a comprehensive overview of the rapidly developing field of molecular electronics. It focuses on our present understanding of the electrical conduction in single-molecule circuits and provides a thorough introduction to the experimental techniques and theoretical concepts. It will also constitute as the first textbook-like introduction to both the experiment and theory of electronic transport through single atoms and molecules. In this sense, this publication will prove invaluable to both researchers and students interested in the field of nanoelectronics and nanoscience in general.Molecular Electronics is self-contained and unified in its presentation. It may be used as a textbook on nanoelectronics by graduate students and advanced undergraduates studying physics and chemistry. In addition, included are previously unpublished material that will help researchers gain a deeper understanding into the basic concepts involved in the field of molecular electronics.Contents:The Birth of Molecular ElectronicsFabrication of Metallic Atomic-Size ContactsContacting Single Molecules: Experimental TechniquesThe Scattering Approach to Phase-Coherent Transport in NanocontactsIntroduction to Green's Function Techniques for Systems in EquilibriumGreen's Functions and Feynman DiagramsNonequilibrium Green's Functions FormalismFormulas of the Electrical Current: Exploiting the Keldysh FormalismElectronic Structure I: Tight-Binding ApproachElectronic Structure II: Density Functional TheoryThe Conductance of a Single AtomSpin-Dependent Transport in Ferromagnetic Atomic ContactsCoherent Transport Through Molecular Junctions I: Basic ConceptsCoherent Transport Through Molecular Junctions II: Test-Bed MoleculesSingle-Molecule Transistors: Coulomb Blockade and Kondo PhysicsVibrationally-Induced Inelastic Current I: ExperimentVibrationally-Induced Inelastic Current II: TheoryThe Hopping Regime and Transport Through DNA MoleculesBeyond Electrical Conductance: Short Noise and Thermal TransportOptical Properties of Current-Carrying Molecular JunctionsWhat is Missing in This Book?Readership: Advanced undergraduate and graduate students in nanoscience and nanotechnology, physics, chemistry, nanoelectronics and molecular electronics.