Everyone is familiar with the amazing performance of a modern smartphone, powered by a billion-plus nanotransistors, each having an active region that is barely a few hundred atoms in length. These lecture notes are about a less appreciated by-product of the microelectronics revolution, namely the deeper understanding of current flow, and device operation that it has enabled, which forms the basis for a new approach to transport problems. The book assumes very little background beyond linear algebra and differential equations, and is intended to be accessible to anyone in any branch of science or engineering. Readers are encouraged to visit the website http://nanohub.org/groups/lnebook to access revisions, corrections, video lectures, tutorials, quizzes and also to join a Q&A forum based on questions from readers.