The results of study of the band structure of single-walled nanotubes, both isolated and embedded into a crystal matrix, and double-walled nanotubes are surveyed. The mathematical apparatus of the linear augmented cylindrical wave (LACW) method is described, and its application to prediction of the electronic properties, semiconducting and metallic, of nanotubes is considered. The method uses the local density functional approximation and the muffin-tin (MT) approximation for the electron potential and is implemented as a quantum-mechanical program package.